Abstract

We chronicle a 15-year development effort of Fresnel incoherent correlation holography (FINCH) since its first description to its current 3D current microscopic wide-field or confocal imaging that doubles optical resolution beyond the Rayleigh limit to about 100 nm in a single snapshot. The path from the original demonstration of FINCH [Opt. Lett. 32, 912 (2007) [CrossRef]  ] to its current picture-perfect imaging of multicolor fluorescent biological specimens and reference test patterns by fluorescence or reflected light imaging is described.

© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. INTRODUCTION

The Digital Holography Symposium in July 2021 celebrates the 15th year of this meeting and the 50th anniversary of the Nobel Prize awarded to Professor Dennis Gabor for his invention of holography. We also celebrate the anniversary of this meeting, originated by Professor Ting-Chung Poon, who also used his scanning holography method to record the first incoherent holographic image of an object emitting incoherent light by imaging fluorescent specimens [1]. After developing the first practical white-light spinning disk confocal microscope [2] that required a series of translated images to record 3D data, we were attracted to scanning holography to obtain 3D images without axial scanning. Our work on scanning holography [3] was followed by the development of the first nonscanning incoherent holography method based on self-interference of light, Fresnel Incoherent Correlation Holography or FINCH [4]. It had the promise of being faster and operationally less complicated than the scanning method that has now been borne out. There have been many steps along the way that have led to the simple current single-shot FINCH methodology we have recently reported [5]. In each step, our goal was to improve upon the previous version, a process that has now resulted in a configuration incorporating a nonquantized birefringent lens (BRL) that creates holograms recorded by a polarized camera that simultaneously captures all the data needed for holographic image reconstruction. The current FINCH configurations are more efficient and create better images than our previous FINCH versions implemented with either a spatial light modulator (SLM) or liquid crystal gradient refractive index (GRIN) lens.

 figure: Fig. 1.

Fig. 1. Principle of increased image resolution by FINCH imaging for [(a), (b), Abbe criteria] single-point and [(c), (d), Rayleigh criteria] two-point imaging. (a) Generalized schematic of classical optical imaging, depicting the effective NA of the image beam ${{\rm NA}_{\rm{beam}}}$ as a function of the image beam size ${R_{\rm{beam}}}$ at the lens and the image distance ${d_i}$, and the size of the classical image spot ${\Delta _i}$; (b) generalized schematic of FINCH imaging, showing the effective NA of the image beam ${{\rm NA}_H}$ increasing by a factor of 2 and the FINCH image spot size decreasing by a factor of 2 to ${\Delta _H}$. The yellow and green lenses and dashed lines represent the two focal lengths ${f_1}$ and ${f_2}$ imparted by the FINCH optics onto the received light from the object. The recorded hologram at the plane ${d_i}$ is computationally reconstructed into an image. (c) Two points imaged by classical methods cannot be distinguished from one another if they are too close. The transverse magnification (${M_T}$, magnification of the image field) and the angular magnification (${M_A}$, magnification of the image spot) are equal to each other. (d) The same two points can be distinguished using FINCH imaging because there is less magnification of each spot, though the field size is magnified to the same extent as a standard optical imager focused to this plane such that the image spots do not change from their original position. Adapted from [5].

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2. GENERAL PRINCIPLES OF FINCH

A detailed description of the principle of FINCH has been recently discussed [5] and is recounted here. FINCH is an imaging technique that can obtain 3D and superresolved information. Referring to Fig. 1(a), classical optical imaging simply requires a lens to receive light from an object and focus that light into an image that is recorded by a camera, magnifying each point in the object by the blurring function known as the point spread function (PSF). Considering a single infinitesimal point, as shown in Fig. 1(a), a given conical angle of the light emitted from the object point, with a finite circular projection on the plane of the lens, is accepted by the lens. The accepted light beam, with radius ${R_{\rm{beam}}}$, along with the distance ${d_i}$ to the image plane, may be thought of as a lens with an effective numerical aperture ${{\rm NA}_{\rm{beam}}}$ equal to ${R_{\rm{beam}}}/{d_i}$, and the image spot size of the object point is inversely proportional to this effective NA. FINCH [4,618] functions by splitting the light received from the object under imaging into two copropagating portions with different focal lengths that interfere with each other and create a hologram of the object [Fig. 1(b)]. The different focal lengths (${f_1}$ and ${f_2}$) are created by a specialized FINCH BRL focusing optic (described later), and the hologram is recorded on a digital camera. Since the recorded holograms are incoherent intensity patterns, they do not reveal the phase of the object, which is critically needed to reconstruct images of high quality. The phase-shifting method [19] of processing several different phases of the recorded hologram has been typically applied to many forms of holography to obtain the complex phase of the hologram. The general method to obtain the complex object field in FINCH holography is to digitally capture and combine several (${\rm{n}}\; \ge \;{{3}}$) phase-shifted raw holograms ${H_{\textit{qn}}}$ of the form

$${H_{\theta n}}\left({{x_h},{y_h};{z_h}} \right) = P\left({{x_h},{y_h};{R_H}} \right)\left\{{\begin{array}{*{20}{c}}{2 + {\rm exp}\left\{{\frac{{i\pi}}{{\lambda {z_r}}}\left[{{{\left({{x_h} - {M_T}{x_s}} \right)}^2} + {{\left({{y_h} - {M_T}{y_s}} \right)}^2} + i{\theta _n}} \right]} \right\}}\\{+ {\rm exp}\left\{{\frac{{- i\pi}}{{\lambda {z_r}}}\left[{{{\left({{x_h} - {M_T}{x_s}} \right)}^2} + {{\left({{y_h} - {M_T}{y_s}} \right)}^2} - i{\theta _n}} \right]} \right\}}\end{array}} \right\},$$
wherein $\lambda$ is the center wavelength of the light band, the subscript $h$ refers to the recording plane and subscript $s$ to the sample plane, ${M_T}$ is the transverse magnification, ${z_r}$ is the reconstruction distance of the hologram, $x$, $y$, and $z$ are Cartesian coordinates, $P({x_h},{y_h};{R_H})$ is a system-dependent pupil function based on the width ${R_H}$ of the recorded raw hologram at the camera plane, and ${\theta _n}$ is a global phase shift applied to the hologram. The $n$ recorded holograms are then composed into a complex-valued hologram ${H_F}$ by superimposing them along with global phase factors using the following Eq. (2):
$${H_F}({x_h},{y_h};{z_h} ) = \mathop\sum\limits_{a = 1}^n {H_{\theta a}}[{\rm exp}({\pm i{\theta _{a - 1}} - \pm i{\theta _{a + 1}}})],$$
wherein $a$ represents the index of the phase shift in the group of raw holograms, ${\theta _{a - 1}} = {\theta _n}$ for $a = {{1}}$, and ${\theta _{a + 1}} = {\theta _1}$ for $a = n$. For example, for a group of four holograms, $a = {{1}}$, 2, 3, 4, with phase shifts 0, ${0.5}\pi$, $\pi$, and ${1.5}\pi$. The superposition process serves to remove the holographic twin image and bias term as well as constant background from the complex hologram, resulting in a representation of the actual phase of the object being imaged.

Following the recovery of the complex hologram by Eq. (2), a simple Fresnel propagation calculation [4,10,11] is sufficient to create a reconstructed focused image of the object using an equation of the form of Eq. (3), describing the formation of the reconstructed image ${I_{\rm{rec}}}$ by convolving the complex hologram ${H_F}$ with an impulse response function (IRF),

$${I_{\rm{rec}}} ({x,y,{z_r}}) = {H_F} ({x,y;{z_h}}){{*}}{\rm IRF} ({x,y,{z_r}}).$$

Referring to Fig. 1(b), the number and size of the fringes in the holograms code for the depth of the object point being reconstructed, conferring on FINCH the ability to encode three-dimensional (3D) information. The self-interference of the light confers a superresolution factor of up to twice the normal optical limit at any given wavelength by incorporating sample information in both light beams that interfere. That is, there are two signal beams rather than the individual signal and reference beams that are characteristic of classical holography. The largest increase in resolution occurs at the plane in which the two differentially focused beams have the same diameter. If the system is arranged so that this plane is at the distance ${d_i}$ from the specialized FINCH optic, it has been shown [10] that the resultant hologram has an effective NA (${{\rm NA}_H}$) of its own, which is equal to ${{2}}{{\rm NA}_{\rm{beam}}}$, the condition shown in Fig. 1(b). Upon the reconstruction calculation, the final spot size of the FINCH image is thus inversely proportional to twice the ${{\rm NA}_{\rm{beam}}}$, leaving it as half the width of the classically imaged spot. Since the lateral magnification of FINCH is the same at any distance away from the lens as in classical imaging, this results in the lateral resolution of FINCH being twice that of classical imaging in this optimal arrangement. This is further illustrated in Figs. 1(c) and 1(d), showing that FINCH does not adhere to the classical Lagrange invariant that describes lateral magnification in classical optical systems. FINCH violates the classical Lagrange invariant and thus improves both single- and two-point lateral resolution [20,21].

 figure: Fig. 2.

Fig. 2. (I) Optical schematic of original reflected light FINCH layout. (II) Phase-shifted lens patterns (a, b, c; 0°, 120°, 240°) and zoomed section thereof (d) showing the randomly assigned constant phase pixels; (e) magnitude and (f) phase of complex FINCH hologram representing object with three axial planes; (g)–(i) reconstructed images of the three planes created from the complex hologram. Adapted from [4].

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3. REFLECTIVE SLM FINCH

The key step that enables FINCH to function as a single-path interferometer is the splitting of light into two copropagating differentially focused beams, as depicted in Fig. 1. The early research on FINCH was performed using a digital SLM that can phase-modulate incident light. In this early work [4], a Fresnel phase pattern was displayed on the SLM to act as a focusing lens on the light received from the sample. Half of the pixels of the SLM displayed this lens pattern, while the other half (randomly assigned) displayed a constant phase, effectively serving as a mirror. In this way, half the light incident on the SLM was altered into a beam that was focused additionally to its previous focus, while half remained a beam that maintained its previous focus unchanged. Importantly, the SLM did not impart any lateral offset to the two beams, so the mutual axis of optical propagation remained unchanged. The two beams interfered with each other due to the self-interference detailed above, and the interference was recorded on a camera. To record three phase-shifted raw holograms as in Eq. (1), three separate SLM patterns were displayed sequentially, as shown in Fig. 2, in which each lens pattern has the same phase curvature with only a constant phase difference of 120° between each. The first proof of principle for FINCH recording was reported for macroscopic reflected-light imaging of three letters at different axial locations illuminated by an incoherent light source and filtered by a fluorescence bandpass filter [4]. This was followed shortly thereafter by a report [6] of FINCH holography on different color-reflected fluorescent lights in another macroscopic sample of three dice with different color fluorescent features.

To prove the capability of FINCH in a more challenging application, a microscope was adapted to direct image light into a FINCH layout incorporating an SLM. This work was reported in [7] and demonstrated the ability to image biological fluorescence samples with FINCH. The refocusing ability of FINCH was apparent, as shown in Fig. 3; microscope calibration beads in layers separated by ${\sim}{{50}}\;{\rm{\unicode{x00B5}{\rm m}}}$ could be resolved by reconstructions from one hologram, as were biological samples that were refocused over a range of ${\sim}{{10}}\;{\rm{\unicode{x00B5}{\rm m}}}$ from a single hologram. Beads in layers ${\sim}{{2}}\;{\rm{\unicode{x00B5}{\rm m}}}$ apart were distinguishable from one another.

 figure: Fig. 3.

Fig. 3. (a) Magnitude of the complex hologram of a sample with three fluorescent beads at different axial depths imaged with the first FINCH holographic microscope; (b)–(d) reconstructed images at three axial planes, each containing one bead in focus. Two beads in (b) and (c) are near each other axially but can still be distinguished by the intensities of their peak reconstructed images. The third bead is ca. 50 µm away from the other two but is still reconstructed from the same raw hologram. (e) The axial line profile through a bead comparing wide field (red) to FINCH (blue). Adapted from [7].

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While these results were quite promising, it was necessary to further refine the understanding of FINCH and elucidate the conditions for obtaining maximum image quality. In several other papers [811], we described the conditions necessary to attain the best-quality FINCH holograms. One advance was the realization that polarization multiplexing [8] could be used advantageously to the random-sampled arrangement used in the early work by taking advantage of the polarized action of the SLM. In this approach, the SLM is placed between two polarizers, termed the input and output polarizers. The light from the object is polarized at the input polarizer to an angle rotated 45° from the polarization axis of the SLM. This allows an entire phase pattern to be displayed on the SLM without random sampling by constant phase pixels, which can cause degradation to the optical performance. Half the light received by the SLM, which had a polarization projection parallel to the SLM polarization axis, was thus focused by the lens pattern; the other half of the light, which had a polarization projection orthogonal to the SLM axis, was passed as if by a mirror. Thus, there were the two required copropagating beams. The output polarizer is rotated by ${\rm{\pm 45}}^\circ$ from the polarization axis of the SLM, and the mutual projections of each of the two beams along the output polarizer axis allow the beams to interfere. The holograms recorded using this strategy had a higher signal to background than the previous method and could be reconstructed into images of higher quality. If a polarizing beam splitter (PBS) is used as the input polarizer to transmit polarized light to the SLM, it is further possible to use the reflected light from the PBS to create a standard image of the same field of view of the sample corresponding to the FINCH image. This is in fact a feature of all the FINCH optical systems described hereafter. In this way, the standard (wide-field or later confocal) image can be captured at exactly the same time for comparative assessment of the FINCH image under identical conditions. Figure 4 shows a reconstructed image of a U.S. Air Force (USAF) test pattern back illuminated by fluorescent light and imaged with wide-field fluorescence imaging and FINCH. The FINCH image has excellent image quality and signal-to-background compared to earlier FINCH images.

 figure: Fig. 4.

Fig. 4. Images of USAF test pattern negative, backlit with fluorescence light at Cy3 wavelength, imaged with a ${{20}} \times$ 0.75 NA objective. The FINCH image was recorded with an SLM located between two polarizers as described in the text. The plot shows superresolution in the FINCH image by the significantly increased visibility (contrast) of the smallest features, near the resolution limited size, for progressively varied iris diameters controlling the effective NA of the lens. Smaller objective back aperture is equivalent to reducing the NA of the lens. Adapted from [9].

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At about the same time as the development of the polarization multiplexing method, several other findings were made. The realization was made that FINCH could be performed using two spherical waves as well as a plane wave and a spherical wave, with shorter optical paths and higher signal-to-background and signal-to-noise in dual spherical-wave FINCH optics [16]. Additionally, the relationships between optical system parameters and 3D depth imaging were elucidated and clarified [10]. Furthermore, the crucial observation that FINCH was capable of optical superresolution was also made [9]. The plot in Fig. 4 shows the visibility (contrast) in the smallest features of the USAF pattern, which approached the minimum resolved feature size that standard optics can resolve with a 0.75 NA objective. We placed an iris at the back pupil of the objective to reduce its NA and captured images at many progressively smaller openings of the iris. We noted, as shown in the plot, that FINCH always produced greater contrast than the wide-field image, and in fact resolved the lines at small iris openings (low NA) when the wide-field image could not do so at all. This observation led to other potential uses of FINCH as a superresolution method beyond purely 3D imaging from a single hologram.

 figure: Fig. 5.

Fig. 5. Images of USAF test pattern negative, backlit with fluorescence light at Cy3 wavelength, imaged with a ${{20}} \times$ 0.75 NA objective on the GRIN-based FINCH system. Note the improved image quality in the FINCH image as compared to the SLM FINCH image in Fig. 4, and similar superresolution as shown by the intensity plots through the smallest features and the visibility (contrast) measurement. Adapted from [12].

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 figure: Fig. 6.

Fig. 6. (a) Wide-field image and (b)–(d) three reconstructed images of different planes of a fluorescently stained pollen grain sample. In the wide-field image, only one plane of the sample is in focus, but three in-focus planes were reconstructed from the FINCH hologram of a single axial position of the captured sample. Adapted from [12].

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4. TRANSMISSION LIQUID CRYSTAL LENS FINCH

While the use of SLMs presents advantages, including the ability to flexibly tailor the critical component of the FINCH process, SLMs also have certain characteristics that can have negative impacts on imaging. Particularly, the lens patterns they display are sensitive to chromatic variation by the light they are acting upon; they must generally be used in a reflective geometry that can render alignment difficult or require the use of lossy beam splitters, and they can suffer several different losses due to pixelation and diffraction effects. To avoid these, we developed a new FINCH apparatus using a liquid crystal GRIN lens [12]. This GRIN lens is an optically clear device that enabled us to switch to an all-transmission-based optical system and addressed many of the negative characteristics of SLMs. Multiple phase-shifted holograms were recorded by using an electrically controlled variable waveplate aligned to one of the beams that added 0°, 120°, or 240° of constant phase. In [12] we showed even higher-quality reconstructed images of the USAF pattern than those created using SLM optics, adapted here in Fig. 5, and were able to do so in a shorter optical path length than had usually been used in SLM FINCH. Figure 6 contains images of several different axial planes of a biological sample that were reconstructed from a single hologram, with image quality at least as good as wide-field fluorescence images, demonstrating the FINCH capability of recording high-quality 3D image space of a real sample in a single hologram.

5. CONFOCAL FINCH

Since the early days of research into FINCH we had interest in applying FINCH holography to confocal imaging. The adoption of the transmissive GRIN lenses also enabled the application of FINCH to spinning disk confocal microscopy. To take best advantage of the superresolving capability of FINCH, it can be beneficial in some contexts to image only a single axial plane of a sample. While this does not take advantage of the large 3D reconstruction ability of FINCH, it can help to improve the image quality of the single focal plane by eliminating out-of-focus light, especially if the sample is an extended or complex sample, and may improve axial resolution as well. A FINCH optical module was adapted to a CARV II spinning disk confocal unit that was itself adapted to the side port of a Zeiss inverted microscope [13,14]. The resulting images (Fig. 7) showed the ability of this method, called CINCH for Confocal INcoherent Correlation Holography, to recover reconstructed images of confocally isolated planes that improved over the corresponding standard confocal images, while maintaining the axial specificity of the confocal images. As was becoming standard for FINCH microscopy in our lab, holographic images of biological samples were recorded that exceeded the quality of corresponding classical (wide-field or confocal) images.

 figure: Fig. 7.

Fig. 7. Imaging two axial planes of a fluorescent pollen sample with (a), (e) wide field; (b), (f) FINCH; (c), (g) confocal; and (d), (h) CINCH. Adapted from [13].

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 figure: Fig. 8.

Fig. 8. Schematics depicting the creation and use of a BRL for FINCH imaging. (a) Orientation of the birefringent axes of the crystal in the transverse plane of the lens blank; (b) creation of colinear differentially focused beams by a BRL; (c) use of a long focal length diverging BRL with a shorter focal length standard lens to create a combined BRL system with two overall converging effective focal lengths; (d) side view of a BRL with a compensating birefringent flat (CBF) used to correct for undesired constant phase shift in the BRL. The arrow and dot indicate orthogonal orientation of the ordinary axes of the lens and flat. Adapted from [15].

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6. TRANSMISSION BIREFRINGENT ALPHA BBO CRYSTAL LENS FINCH

The use of the liquid crystal GRIN lenses proved the benefits that could be obtained by using only transmission optics in the FINCH optical path. To achieve the absolute maximum image quality in all ways, it became clear that it was necessary to use components that introduced the fewest deviations from standard classical transmission optics. Thus, we constructed several transmission BRLs from birefringent crystals, including calcite and alpha-BBO, and used these to effect the polarization-based colinear beam splitting [15]. These materials offer high optical clarity in the visible, UV-B, and NIR ranges, and since they can be readily cut into transmission lenses, they can easily be matched to other additional lenses to correct for chromatic variations or other aberrations, much as any other lens can be. This enables FINCH using BRLs to achieve the highest optical beam quality at all stages of the optical path without any of the defects that can be imparted by pixelated, quantized, or diffractive optics that are otherwise commonly used for FINCH. These BRL FINCH systems are also flexible due to the ability to pair the BRL with other lenses to adjust the total combined focal lengths, as described in [15].

A BRL lens can be prepared for FINCH by cutting the optical blank so that the birefringent axes of the crystal lie in the transverse plane of the lens, as shown in Fig. 8. The blank is then shaped and polished to the desired curvature. For the main FINCH system reported in [15], the BRL was made from alpha-BBO due to its ready availability, high birefringence, and environmental stability. The BBO lens was created as a relatively long focal length diverging lens and paired with a well-corrected shorter focal length converging lens in order to produce a combined lens system with good optical correction and a relatively closely spaced pair of focal lengths. To achieve the polarization multiplexed beam splitting for FINCH, the lens is then placed with its birefringent axes rotated ${\rm{\pm 45}}^\circ$ to the polarization of the light received from the sample, so that the light has an equal projection on each focal length of the BRL. The BRL thus produces two differentially focused colinear beams. An output polarizer after the BRL serves to recombine the two beams and enable their interference to be recorded on a camera. As with the GRIN FINCH system, an electrically variable wave plate was used to shift the phase of one of the beams in order to gather the different phase-shifted raw holograms.

 figure: Fig. 9.

Fig. 9. (a), (c) Wide-field and (b), (d) FINCH imaging of three different stained Golgi proteins in a labeled cell. The superresolving character of the FINCH image is seen in the increased image contrast and better localization of the imaged proteins in their own locations and not overlapped on the other proteins locations. Adapted from [15].

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The BRL-based FINCH fluorescence microscope system was shown to achieve ${{2}} \times$ resolution improvement in FINCH images compared to wide-field images after deconvolution of the images. A sample of 100 nm fluorescent calibration beads imaged at 590 nm fluorescence emission was measured as 149 nm, compared to 287 nm for the exact same beads in the wide-field image [15]. As shown in Fig. 9, a three-color biological sample containing three fluorescently labeled Golgi proteins was also imaged at ${{100}} \times$ objective magnification, the highest magnification incoherent holograms of which we are aware, and produced images of comparable or better quality than those produced by a commercial structured illumination microscopy (SIM) system at a similar magnification (Supplementary information of [15]).

 figure: Fig. 10.

Fig. 10. Single-shot BRL FINCH imaging principle. All necessary optical components for single-shot FINCH are shown in this schematic. (a) Polarized image light originating from the object is provided to the BRL. The BRL, which is of high optical quality, splits the incoming image beam into a linearly orthogonally polarized pair of copropagating beams with differing focal lengths. The beams are converted to orthogonal circular polarizations by the QWP and subsequently interfere with one another to create a hologram that is recorded by a camera with multiplexed micropolarizers. Four interspersed phase-shifted holograms are recorded simultaneously. (b) Schematic of the camera pixels overlaid with the interspersed micropolarizer array; the micropolarizer grid has four equally spaced polarizer orientations (0, ${0.5}\pi$, $\pi$, and ${1.5}\pi$ rad) precisely arranged on the CMOS die in a repeating square pattern. (c) (i) The recorded hologram is deinterspersed by a computer in one step into four subsampled phases, (ii) then interpolated by nearest neighbor interpolation, (iii) followed by superpositioning to create the complex hologram (iv) before being propagated to create the reconstructed image. Adapted from [5].

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7. SINGLE-SHOT FINCH

After the BRL FINCH system produced superresolved images on a par with a much more complicated and expensive system, further demonstrating FINCH’s potential, the next factor to optimize was the number of exposures required. While three sequential phase-shifted recordings were used for most of the development history of FINCH, it was clear that using a single recorded hologram would be even better due to the lower excitation energy dose that could be used as well as the elimination of artifacts that can accrue during multiple captures due to factors including shot-to-shot instability in the illumination intensity, intershot photobleaching and/or sample motion, and reproducibility error of the phase-shifting optic. A further factor that must be addressed is the need to account for and calibrate for chromatic variation of the phase-shifting optic, either SLM or electrically variable wave plate. In a fluorescence microscopy system with 40–50 nm bandwidth per dye, the calibration accuracy of the phase shift for light in the fluorescence band away from the calibrated wavelength decreases to a degree sufficient to reduce the performance of FINCH below its full potential. While different calibrations can be created for the wavelength at the center of any given light band, the applied phase shift will still have some chromatic error from one end of the light band to the other, which can cause subtle changes in the quality of the resultant images [17].

Recently we reported [5] a FINCH method that modifies the BRL-based method by recording four phase-shifted holograms simultaneously in a single exposure. We added a broadband quarter-wave plate (QWP) after the BRL, and a polarized CMOS sensor to record the holograms in place of the scientific CMOS camera to record the holograms, as shown in Fig. 10. For two orthogonally circularly polarized light beams, the phase of the interference between the beams is controlled by the relative angle of the polarizer that projects the two beams back along a common polarization axis. We created a new FINCH microscope with FINCH optics, as shown in Fig. 10(a): linearly polarized light from the sample is received by a BRL with two polarization-dependent focal lengths aligned at ${\rm{\pm 45}}^\circ$ to the polarization of the incoming light, creating a pair of differentially focused copropagating linearly orthogonally polarized light beams as described above. The QWP positioned after the BRL turns the copropagating linearly orthogonally polarized beams into circularly orthogonally polarized beams, and the polarized CMOS sensor, the pixels of which are overlaid with a micropolarizer grid incorporating four different polarization orientations [Fig. 10(b)],

 figure: Fig. 11.

Fig. 11. Schematic of the FINCH/CINCH microscope. ${{\rm{L}}_O}$, objective lens; ${{\rm{L}}_1}$, ${{\rm{L}}_2}$, relay lenses; D, dichroic mirror to isolate fluorescence excitation from emission light; PBS, polarizing beam splitter; P, S, transmitted and reflected linear polarizations; BRL, birefringent lens; QWP, quarter-wave plate; ${{\rm{L}}_3}$, standard microscope tube lens. All of the components critical to the FINCH technique are contained in the shaded area. All other components are extrinsic to the FINCH technique and are present only to serve as the basic microscope optics upon which the FINCH system optics is based to create the superresolved image. The FINCH system optics could be added to any microscope optical system. Insertion of the spinning pinhole disk between the ${{\rm{L}}_1}$, ${{\rm{L}}_2}$ relay lenses converts the system into a confocal FINCH system in which a single image plane is imaged by the FINCH optics (CINCH). With the spinning pinhole disk in place, the standard camera records a confocal image. Adapted from [5].

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simultaneously records four precisely phase-shifted holograms in quadrature. The simultaneously recorded raw holograms are deinterspersed into four raw holograms as in Fig. 10(c), each containing pixels of only a single-phase shift value, as in Eq. (1). The raw holograms are then interpolated by nearest neighbor or cubic interpolation to fill in the blank pixels in each. The phase-shifted recorded holograms are then processed into reconstructed images by Eqs. (2) and (3) above. As can be seen in Fig. 11 showing a schematic of the FINCH microscope constructed on these principles, this results in a FINCH system that is extremely simple, stable, and compact, with only three specialized components required for FINCH. The system is additionally free of the need for sequential exposure due to the multiplexed phase recording, and free of the need for chromatic calibration for phase shifting as well due to the broadband design of the QWP we used, which shifts all wavelengths within any image light band by the quarter wave necessary for phase shifting in formation of the FINCH interference pattern. The holograms created at any wavelength or bandwidth are thus as optically perfect and achromatic as they can be. As described above, the single-shot FINCH system can also be easily used for CINCH imaging by the insertion of a spinning Nipkow disk at the relay conjugate image plane, capitalizing on the improved axial resolution of confocal microscopy [13,14].
 figure: Fig. 12.

Fig. 12. FINCH lateral resolution of 100 nm subresolution fluorescent beads imaged with a ${{60}} \times$ 1.49 NA Nikon objective at 590 nm emission wavelength significantly exceeds the wide-field resolution of corresponding beads. (a) Wide-field and (b) FINCH images of the identical image field of 100 nm (nominal) beads, with insets showing a magnified detail; (c) plot of two closely spaced beads showing greatly improved two-point resolution with FINCH compared with wide field. The green arrows in (a), (b) point out the bead pair shown in the profiles in this plot. (d) Plot of average bead lateral FWHM made from randomly selected beads; (e) plot of average bead axial FWHM measured by physically stepping the sample through the objective focus over the indicated range in 100 nm steps. Adapted from [5].

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 figure: Fig. 13.

Fig. 13. (a), (b) Deconvolved confocal and CINCH images of microtubules. Red outlines indicate example comparison areas in which the superresolved CINCH image reveal more detail than is seen in the confocal image. (c) Plots of microtubule lateral FWHM from the deconvolved images. Adapted from [5].

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 figure: Fig. 14.

Fig. 14. Reflected light FINCH imaging. Original (nondeconvolved) (a) wide-field and (b) FINCH reflected light images of a chrome USAF test pattern printed on a glass slide, taken with a ${{10}} \times$ 0.3 NA objective under 465 nm incoherent illumination. Adapted from [5].

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 figure: Fig. 15.

Fig. 15. FINCH and comparative wide-field fluorescence imaging (520 nm emission) of the Argolight SIM resolution standard. Images were taken simultaneously using a ${{60}} \times$ 1.49 NA objective and the microscope described in [5]. The plots are taken through the line pair features indicated by the colored lines across the image. The approximate classical Rayleigh limit is indicated on the wide-field plot. The smallest line pair separation (best two-point resolution) achieved with the FINCH image is indicated on the FINCH plot.

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We used the new single-shot system to capture FINCH holograms of 100 nm beads (Fig. 12) and CINCH holograms of boron-dipyrromethene (BODIPY) stained microtubules (Fig. 13), both of which are samples often used to test the FWHM of superresolved imaging systems. In both samples, the reconstructed images possessed FWHM comparable to the Zeiss Airyscan microscope and SIM microscopes [5]. A random sample of 100 nm beads, recorded with a ${{60}} \times$ objective, was measured to have a FWHM of ${\sim}{{130}}\;{\rm{nm}}$ at an imaging wavelength of 590 nm, which corresponds to ${\sim}{{115}}\;{\rm{nm}}$ at the 520 nm wavelength that was reported for an analogous sample image with the Zeiss Airyscan instrument. The two-point resolution was also significantly improved over a corresponding wide-field image taken at the same time, as shown in Fig. 12(c). The axial resolution was approximately the same as a standard wide-field image. The microtubules were measured as having a width of 118 nm, similar to the value of 120 nm recorded for a similar sample imaged on a commercial SIM system. For both samples, the FINCH/CINCH images performed better than iSIM, one of the leading image-scanning type superresolution instruments.

To further demonstrate that the high image quality of FINCH is not limited to fluorescence imaging with high NA objectives, a reflective USAF pattern (Max Levy) was imaged in the FINCH microscope with 465 nm reflected light, using a ${{10}}\; \times$ 0.3 NA objective. The results, without deconvolution, are shown in Fig. 14. Note that the FINCH image is of high quality, with sharp edges of the features and contrast as high as the wide-field image, and with no degradation due to speckle as might be expected from holographic reflectance imaging. In fact, careful inspection reveals that the defects in the reflective pattern are imaged more clearly in the FINCH image than in the wide-field image. The application of FINCH to reflected light imaging has many potential applications beyond biomedical microscopy, including consumer camera imaging and metrology.

To further set FINCH in context compared to other superresolution microscopy systems, we also have imaged the Argolight SIM resolution test standard. The pattern of interest for this sample is a series of fluorescent lines embedded in a glass matrix. The lines are arranged in a series, with pairs of lines separated from each other by progressively less distance in increments of 30 nm, from 390 nm separation to 0 nm separation, to serve as a test for two-point resolution that can be compared across different instruments. We imaged this sample in the instrument described in [5] at a 520 nm emission wavelength with a ${{60}} \times$ 1.49 NA oil immersion objective without the confocal disk. The resulting image is shown in Fig. 15, comparing a wide-field image to the FINCH image. The images and plots show that the line pairs are resolved at 210–240 nm in the wide-field image, though they are not resolved to the full Rayleigh criterion. However, in the FINCH image, the line pairs with 120 nm or more separation are well resolved by the Rayleigh criterion. The line pair at 90 nm separation is nearly Rayleigh-resolved and is as well resolved as the wide-field image of the 300-nm separated line pair. This result, on a challenging sample, was obtained with a single snapshot confirming the ability of FINCH as an effective (as well as simple and inexpensive) superresolution technique.

8. CONCLUSION AND THE FUTURE

With the history of development behind it, and the recent adoptions of the BRL optical system and the single-shot recording method, FINCH has become a truly simple, versatile, stable, broadband incoherent holographic superresolution imaging system. We should point out that there are many other opportunities opened by our invention of the single-shot high imaging quality BRL FINCH system, not only for FINCH holographic microscopy but also for many other applications wherein a solid-state single-path interferometric system might be useful, including biomedical screening and industrial metrology. With new developments in image processing and birefringent and other manifocal lenses being made frequently, we anticipate the performance and capabilities of FINCH will expand.

Funding

CellOptic, Inc.

Disclosures

GB: CellOptic, Inc. (I, E, P). NS: CellOptic, (I, E, P). CellOptic, Inc. has a number of issued and pending U.S. and international patents on FINCH and related material.

Data Availability

Original images as captured by the cameras are available upon request. Processed images are available upon request. Indices of the beads and microtubules measured for FWHM are available on request.

REFERENCES

1. T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional fluorescence microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995). [CrossRef]  

2. G. Brooker, S. McDonald, G. Adams, and J. Brooker, “Microscope attachment for high precision and efficient imaging,” U.S. patent 6,147,798 A (14 November 2000).

3. J. Rosen, G. Indebetouw, and G. Brooker, “Homodyne scanning holography,” Opt. Express 14, 4280–4285 (2006). [CrossRef]  

4. J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32, 912–914 (2007). [CrossRef]  

5. N. Siegel and G. Brooker, “Single shot holographic super-resolution microscopy,” Opt. Express 29, 15953–15968 (2021). [CrossRef]  

6. J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express 15, 2244–2250 (2007). [CrossRef]  

7. J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008). [CrossRef]  

8. G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express 19, 5047–5062 (2011). [CrossRef]  

9. J. Rosen, N. Siegel, and G. Brooker, “Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging,” Opt. Express 19, 26249–26268 (2011). [CrossRef]  

10. N. Siegel, J. Rosen, and G. Brooker, “Reconstruction of objects above and below the objective focal plane with dimensional fidelity by FINCH fluorescence microscopy,” Opt. Express 20, 19822–19835 (2012). [CrossRef]  

11. N. Siegel, J. Rosen, and G. Brooker, “Faithful reconstruction of digital holograms captured by FINCH using a Hamming window function in the Fresnel propagation,” Opt. Lett. 38, 3922–3925 (2013). [CrossRef]  

12. G. Brooker, N. Siegel, J. Rosen, N. Hashimoto, M. Kurihara, and A. Tanabe, “In-line FINCH super resolution digital holographic fluorescence microscopy using a high efficiency transmission liquid crystal GRIN lens,” Opt. Lett. 38, 5264–5267 (2013). [CrossRef]  

13. N. Siegel and G. Brooker, “Improved axial resolution of FINCH fluorescence microscopy when combined with spinning disk confocal microscopy,” Opt. Express 22, 22298–22307 (2014). [CrossRef]  

14. N. Siegel, B. Storrie, M. Bruce, and G. Brooker, “CINCH (confocal incoherent correlation holography) high spatial resolution super resolution fluorescence microscopy based upon FINCH (Fresnel incoherent correlation holography),” Proc. SPIE 9336, 93360S (2015). [CrossRef]  

15. N. Siegel, V. Lupashin, B. Storrie, and G. Brooker, “High-magnification super-resolution FINCH microscopy using birefringent crystal lens interferometers,” Nat. Photonics 10, 802–808 (2016). [CrossRef]  

16. B. Katz, J. Rosen, R. Kelner, and G. Brooker, “Enhanced resolution and throughput of Fresnel incoherent correlation holography (FINCH) using dual diffractive lenses on a spatial light modulator (SLM),” Opt. Express 20, 9109–9121 (2012). [CrossRef]  

17. P. Bouchal and Z. Bouchal, “Concept of coherence aperture and pathways toward white light high-resolution correlation imaging,” New J. Phys. 15, 123002 (2013). [CrossRef]  

18. P. Bouchal and Z. Bouchal, “Wide-field common-path incoherent correlation microscopy with a perfect overlapping of interfering beams,” J. Eur. Opt. Soc. 8, 13011 (2013). [CrossRef]  

19. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997). [CrossRef]  

20. X. Lai, S. Zeng, X. Lv, J. Yuan, and L. Fu, “Violation of the Lagrange invariant in an optical imaging system,” Opt. Lett. 38, 1896–1898 (2013). [CrossRef]  

21. J. Rosen and R. Kelner, “Modified Lagrange invariants and their role in determining transverse and axial imaging resolutions of self-interference incoherent holographic systems,” Opt. Express 22, 29048–29066 (2014). [CrossRef]  

References

  • View by:

  1. T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional fluorescence microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
    [Crossref]
  2. G. Brooker, S. McDonald, G. Adams, and J. Brooker, “Microscope attachment for high precision and efficient imaging,” U.S. patent6,147,798 A (14November2000).
  3. J. Rosen, G. Indebetouw, and G. Brooker, “Homodyne scanning holography,” Opt. Express 14, 4280–4285 (2006).
    [Crossref]
  4. J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32, 912–914 (2007).
    [Crossref]
  5. N. Siegel and G. Brooker, “Single shot holographic super-resolution microscopy,” Opt. Express 29, 15953–15968 (2021).
    [Crossref]
  6. J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express 15, 2244–2250 (2007).
    [Crossref]
  7. J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008).
    [Crossref]
  8. G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express 19, 5047–5062 (2011).
    [Crossref]
  9. J. Rosen, N. Siegel, and G. Brooker, “Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging,” Opt. Express 19, 26249–26268 (2011).
    [Crossref]
  10. N. Siegel, J. Rosen, and G. Brooker, “Reconstruction of objects above and below the objective focal plane with dimensional fidelity by FINCH fluorescence microscopy,” Opt. Express 20, 19822–19835 (2012).
    [Crossref]
  11. N. Siegel, J. Rosen, and G. Brooker, “Faithful reconstruction of digital holograms captured by FINCH using a Hamming window function in the Fresnel propagation,” Opt. Lett. 38, 3922–3925 (2013).
    [Crossref]
  12. G. Brooker, N. Siegel, J. Rosen, N. Hashimoto, M. Kurihara, and A. Tanabe, “In-line FINCH super resolution digital holographic fluorescence microscopy using a high efficiency transmission liquid crystal GRIN lens,” Opt. Lett. 38, 5264–5267 (2013).
    [Crossref]
  13. N. Siegel and G. Brooker, “Improved axial resolution of FINCH fluorescence microscopy when combined with spinning disk confocal microscopy,” Opt. Express 22, 22298–22307 (2014).
    [Crossref]
  14. N. Siegel, B. Storrie, M. Bruce, and G. Brooker, “CINCH (confocal incoherent correlation holography) high spatial resolution super resolution fluorescence microscopy based upon FINCH (Fresnel incoherent correlation holography),” Proc. SPIE 9336, 93360S (2015).
    [Crossref]
  15. N. Siegel, V. Lupashin, B. Storrie, and G. Brooker, “High-magnification super-resolution FINCH microscopy using birefringent crystal lens interferometers,” Nat. Photonics 10, 802–808 (2016).
    [Crossref]
  16. B. Katz, J. Rosen, R. Kelner, and G. Brooker, “Enhanced resolution and throughput of Fresnel incoherent correlation holography (FINCH) using dual diffractive lenses on a spatial light modulator (SLM),” Opt. Express 20, 9109–9121 (2012).
    [Crossref]
  17. P. Bouchal and Z. Bouchal, “Concept of coherence aperture and pathways toward white light high-resolution correlation imaging,” New J. Phys. 15, 123002 (2013).
    [Crossref]
  18. P. Bouchal and Z. Bouchal, “Wide-field common-path incoherent correlation microscopy with a perfect overlapping of interfering beams,” J. Eur. Opt. Soc. 8, 13011 (2013).
    [Crossref]
  19. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [Crossref]
  20. X. Lai, S. Zeng, X. Lv, J. Yuan, and L. Fu, “Violation of the Lagrange invariant in an optical imaging system,” Opt. Lett. 38, 1896–1898 (2013).
    [Crossref]
  21. J. Rosen and R. Kelner, “Modified Lagrange invariants and their role in determining transverse and axial imaging resolutions of self-interference incoherent holographic systems,” Opt. Express 22, 29048–29066 (2014).
    [Crossref]

2021 (1)

2016 (1)

N. Siegel, V. Lupashin, B. Storrie, and G. Brooker, “High-magnification super-resolution FINCH microscopy using birefringent crystal lens interferometers,” Nat. Photonics 10, 802–808 (2016).
[Crossref]

2015 (1)

N. Siegel, B. Storrie, M. Bruce, and G. Brooker, “CINCH (confocal incoherent correlation holography) high spatial resolution super resolution fluorescence microscopy based upon FINCH (Fresnel incoherent correlation holography),” Proc. SPIE 9336, 93360S (2015).
[Crossref]

2014 (2)

2013 (5)

2012 (2)

2011 (2)

2008 (1)

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008).
[Crossref]

2007 (2)

2006 (1)

1997 (1)

1995 (1)

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional fluorescence microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[Crossref]

Adams, G.

G. Brooker, S. McDonald, G. Adams, and J. Brooker, “Microscope attachment for high precision and efficient imaging,” U.S. patent6,147,798 A (14November2000).

Bouchal, P.

P. Bouchal and Z. Bouchal, “Concept of coherence aperture and pathways toward white light high-resolution correlation imaging,” New J. Phys. 15, 123002 (2013).
[Crossref]

P. Bouchal and Z. Bouchal, “Wide-field common-path incoherent correlation microscopy with a perfect overlapping of interfering beams,” J. Eur. Opt. Soc. 8, 13011 (2013).
[Crossref]

Bouchal, Z.

P. Bouchal and Z. Bouchal, “Wide-field common-path incoherent correlation microscopy with a perfect overlapping of interfering beams,” J. Eur. Opt. Soc. 8, 13011 (2013).
[Crossref]

P. Bouchal and Z. Bouchal, “Concept of coherence aperture and pathways toward white light high-resolution correlation imaging,” New J. Phys. 15, 123002 (2013).
[Crossref]

Brooker, G.

N. Siegel and G. Brooker, “Single shot holographic super-resolution microscopy,” Opt. Express 29, 15953–15968 (2021).
[Crossref]

N. Siegel, V. Lupashin, B. Storrie, and G. Brooker, “High-magnification super-resolution FINCH microscopy using birefringent crystal lens interferometers,” Nat. Photonics 10, 802–808 (2016).
[Crossref]

N. Siegel, B. Storrie, M. Bruce, and G. Brooker, “CINCH (confocal incoherent correlation holography) high spatial resolution super resolution fluorescence microscopy based upon FINCH (Fresnel incoherent correlation holography),” Proc. SPIE 9336, 93360S (2015).
[Crossref]

N. Siegel and G. Brooker, “Improved axial resolution of FINCH fluorescence microscopy when combined with spinning disk confocal microscopy,” Opt. Express 22, 22298–22307 (2014).
[Crossref]

N. Siegel, J. Rosen, and G. Brooker, “Faithful reconstruction of digital holograms captured by FINCH using a Hamming window function in the Fresnel propagation,” Opt. Lett. 38, 3922–3925 (2013).
[Crossref]

G. Brooker, N. Siegel, J. Rosen, N. Hashimoto, M. Kurihara, and A. Tanabe, “In-line FINCH super resolution digital holographic fluorescence microscopy using a high efficiency transmission liquid crystal GRIN lens,” Opt. Lett. 38, 5264–5267 (2013).
[Crossref]

N. Siegel, J. Rosen, and G. Brooker, “Reconstruction of objects above and below the objective focal plane with dimensional fidelity by FINCH fluorescence microscopy,” Opt. Express 20, 19822–19835 (2012).
[Crossref]

B. Katz, J. Rosen, R. Kelner, and G. Brooker, “Enhanced resolution and throughput of Fresnel incoherent correlation holography (FINCH) using dual diffractive lenses on a spatial light modulator (SLM),” Opt. Express 20, 9109–9121 (2012).
[Crossref]

G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express 19, 5047–5062 (2011).
[Crossref]

J. Rosen, N. Siegel, and G. Brooker, “Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging,” Opt. Express 19, 26249–26268 (2011).
[Crossref]

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008).
[Crossref]

J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express 15, 2244–2250 (2007).
[Crossref]

J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32, 912–914 (2007).
[Crossref]

J. Rosen, G. Indebetouw, and G. Brooker, “Homodyne scanning holography,” Opt. Express 14, 4280–4285 (2006).
[Crossref]

G. Brooker, S. McDonald, G. Adams, and J. Brooker, “Microscope attachment for high precision and efficient imaging,” U.S. patent6,147,798 A (14November2000).

Brooker, J.

G. Brooker, S. McDonald, G. Adams, and J. Brooker, “Microscope attachment for high precision and efficient imaging,” U.S. patent6,147,798 A (14November2000).

Bruce, M.

N. Siegel, B. Storrie, M. Bruce, and G. Brooker, “CINCH (confocal incoherent correlation holography) high spatial resolution super resolution fluorescence microscopy based upon FINCH (Fresnel incoherent correlation holography),” Proc. SPIE 9336, 93360S (2015).
[Crossref]

Doh, K. B.

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional fluorescence microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[Crossref]

Fu, L.

Hashimoto, N.

Indebetouw, G.

Katz, B.

Kelner, R.

Kurihara, M.

Lai, X.

Lupashin, V.

N. Siegel, V. Lupashin, B. Storrie, and G. Brooker, “High-magnification super-resolution FINCH microscopy using birefringent crystal lens interferometers,” Nat. Photonics 10, 802–808 (2016).
[Crossref]

Lv, X.

McDonald, S.

G. Brooker, S. McDonald, G. Adams, and J. Brooker, “Microscope attachment for high precision and efficient imaging,” U.S. patent6,147,798 A (14November2000).

Poon, T.-C.

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional fluorescence microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[Crossref]

Rosen, J.

J. Rosen and R. Kelner, “Modified Lagrange invariants and their role in determining transverse and axial imaging resolutions of self-interference incoherent holographic systems,” Opt. Express 22, 29048–29066 (2014).
[Crossref]

N. Siegel, J. Rosen, and G. Brooker, “Faithful reconstruction of digital holograms captured by FINCH using a Hamming window function in the Fresnel propagation,” Opt. Lett. 38, 3922–3925 (2013).
[Crossref]

G. Brooker, N. Siegel, J. Rosen, N. Hashimoto, M. Kurihara, and A. Tanabe, “In-line FINCH super resolution digital holographic fluorescence microscopy using a high efficiency transmission liquid crystal GRIN lens,” Opt. Lett. 38, 5264–5267 (2013).
[Crossref]

N. Siegel, J. Rosen, and G. Brooker, “Reconstruction of objects above and below the objective focal plane with dimensional fidelity by FINCH fluorescence microscopy,” Opt. Express 20, 19822–19835 (2012).
[Crossref]

B. Katz, J. Rosen, R. Kelner, and G. Brooker, “Enhanced resolution and throughput of Fresnel incoherent correlation holography (FINCH) using dual diffractive lenses on a spatial light modulator (SLM),” Opt. Express 20, 9109–9121 (2012).
[Crossref]

G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express 19, 5047–5062 (2011).
[Crossref]

J. Rosen, N. Siegel, and G. Brooker, “Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging,” Opt. Express 19, 26249–26268 (2011).
[Crossref]

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008).
[Crossref]

J. Rosen and G. Brooker, “Digital spatially incoherent Fresnel holography,” Opt. Lett. 32, 912–914 (2007).
[Crossref]

J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express 15, 2244–2250 (2007).
[Crossref]

J. Rosen, G. Indebetouw, and G. Brooker, “Homodyne scanning holography,” Opt. Express 14, 4280–4285 (2006).
[Crossref]

Schilling, B. W.

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional fluorescence microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[Crossref]

Shinoda, K.

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional fluorescence microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[Crossref]

Siegel, N.

N. Siegel and G. Brooker, “Single shot holographic super-resolution microscopy,” Opt. Express 29, 15953–15968 (2021).
[Crossref]

N. Siegel, V. Lupashin, B. Storrie, and G. Brooker, “High-magnification super-resolution FINCH microscopy using birefringent crystal lens interferometers,” Nat. Photonics 10, 802–808 (2016).
[Crossref]

N. Siegel, B. Storrie, M. Bruce, and G. Brooker, “CINCH (confocal incoherent correlation holography) high spatial resolution super resolution fluorescence microscopy based upon FINCH (Fresnel incoherent correlation holography),” Proc. SPIE 9336, 93360S (2015).
[Crossref]

N. Siegel and G. Brooker, “Improved axial resolution of FINCH fluorescence microscopy when combined with spinning disk confocal microscopy,” Opt. Express 22, 22298–22307 (2014).
[Crossref]

N. Siegel, J. Rosen, and G. Brooker, “Faithful reconstruction of digital holograms captured by FINCH using a Hamming window function in the Fresnel propagation,” Opt. Lett. 38, 3922–3925 (2013).
[Crossref]

G. Brooker, N. Siegel, J. Rosen, N. Hashimoto, M. Kurihara, and A. Tanabe, “In-line FINCH super resolution digital holographic fluorescence microscopy using a high efficiency transmission liquid crystal GRIN lens,” Opt. Lett. 38, 5264–5267 (2013).
[Crossref]

N. Siegel, J. Rosen, and G. Brooker, “Reconstruction of objects above and below the objective focal plane with dimensional fidelity by FINCH fluorescence microscopy,” Opt. Express 20, 19822–19835 (2012).
[Crossref]

J. Rosen, N. Siegel, and G. Brooker, “Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging,” Opt. Express 19, 26249–26268 (2011).
[Crossref]

G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express 19, 5047–5062 (2011).
[Crossref]

Storrie, B.

N. Siegel, V. Lupashin, B. Storrie, and G. Brooker, “High-magnification super-resolution FINCH microscopy using birefringent crystal lens interferometers,” Nat. Photonics 10, 802–808 (2016).
[Crossref]

N. Siegel, B. Storrie, M. Bruce, and G. Brooker, “CINCH (confocal incoherent correlation holography) high spatial resolution super resolution fluorescence microscopy based upon FINCH (Fresnel incoherent correlation holography),” Proc. SPIE 9336, 93360S (2015).
[Crossref]

Suzuki, Y.

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional fluorescence microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[Crossref]

Tanabe, A.

Wang, V.

Wu, M. H.

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional fluorescence microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[Crossref]

Yamaguchi, I.

Yuan, J.

Zeng, S.

Zhang, T.

J. Eur. Opt. Soc. (1)

P. Bouchal and Z. Bouchal, “Wide-field common-path incoherent correlation microscopy with a perfect overlapping of interfering beams,” J. Eur. Opt. Soc. 8, 13011 (2013).
[Crossref]

Nat. Photonics (2)

N. Siegel, V. Lupashin, B. Storrie, and G. Brooker, “High-magnification super-resolution FINCH microscopy using birefringent crystal lens interferometers,” Nat. Photonics 10, 802–808 (2016).
[Crossref]

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2, 190–195 (2008).
[Crossref]

New J. Phys. (1)

P. Bouchal and Z. Bouchal, “Concept of coherence aperture and pathways toward white light high-resolution correlation imaging,” New J. Phys. 15, 123002 (2013).
[Crossref]

Opt. Eng. (1)

T.-C. Poon, K. B. Doh, B. W. Schilling, M. H. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional fluorescence microscopy by optical scanning holography,” Opt. Eng. 34, 1338–1344 (1995).
[Crossref]

Opt. Express (9)

J. Rosen, G. Indebetouw, and G. Brooker, “Homodyne scanning holography,” Opt. Express 14, 4280–4285 (2006).
[Crossref]

G. Brooker, N. Siegel, V. Wang, and J. Rosen, “Optimal resolution in Fresnel incoherent correlation holographic fluorescence microscopy,” Opt. Express 19, 5047–5062 (2011).
[Crossref]

J. Rosen, N. Siegel, and G. Brooker, “Theoretical and experimental demonstration of resolution beyond the Rayleigh limit by FINCH fluorescence microscopic imaging,” Opt. Express 19, 26249–26268 (2011).
[Crossref]

N. Siegel, J. Rosen, and G. Brooker, “Reconstruction of objects above and below the objective focal plane with dimensional fidelity by FINCH fluorescence microscopy,” Opt. Express 20, 19822–19835 (2012).
[Crossref]

B. Katz, J. Rosen, R. Kelner, and G. Brooker, “Enhanced resolution and throughput of Fresnel incoherent correlation holography (FINCH) using dual diffractive lenses on a spatial light modulator (SLM),” Opt. Express 20, 9109–9121 (2012).
[Crossref]

N. Siegel and G. Brooker, “Single shot holographic super-resolution microscopy,” Opt. Express 29, 15953–15968 (2021).
[Crossref]

J. Rosen and G. Brooker, “Fluorescence incoherent color holography,” Opt. Express 15, 2244–2250 (2007).
[Crossref]

N. Siegel and G. Brooker, “Improved axial resolution of FINCH fluorescence microscopy when combined with spinning disk confocal microscopy,” Opt. Express 22, 22298–22307 (2014).
[Crossref]

J. Rosen and R. Kelner, “Modified Lagrange invariants and their role in determining transverse and axial imaging resolutions of self-interference incoherent holographic systems,” Opt. Express 22, 29048–29066 (2014).
[Crossref]

Opt. Lett. (5)

Proc. SPIE (1)

N. Siegel, B. Storrie, M. Bruce, and G. Brooker, “CINCH (confocal incoherent correlation holography) high spatial resolution super resolution fluorescence microscopy based upon FINCH (Fresnel incoherent correlation holography),” Proc. SPIE 9336, 93360S (2015).
[Crossref]

Other (1)

G. Brooker, S. McDonald, G. Adams, and J. Brooker, “Microscope attachment for high precision and efficient imaging,” U.S. patent6,147,798 A (14November2000).

Data Availability

Original images as captured by the cameras are available upon request. Processed images are available upon request. Indices of the beads and microtubules measured for FWHM are available on request.

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Figures (15)

Fig. 1.
Fig. 1. Principle of increased image resolution by FINCH imaging for [(a), (b), Abbe criteria] single-point and [(c), (d), Rayleigh criteria] two-point imaging. (a) Generalized schematic of classical optical imaging, depicting the effective NA of the image beam ${{\rm NA}_{\rm{beam}}}$ as a function of the image beam size ${R_{\rm{beam}}}$ at the lens and the image distance ${d_i}$ , and the size of the classical image spot ${\Delta _i}$ ; (b) generalized schematic of FINCH imaging, showing the effective NA of the image beam ${{\rm NA}_H}$ increasing by a factor of 2 and the FINCH image spot size decreasing by a factor of 2 to ${\Delta _H}$ . The yellow and green lenses and dashed lines represent the two focal lengths ${f_1}$ and ${f_2}$ imparted by the FINCH optics onto the received light from the object. The recorded hologram at the plane ${d_i}$ is computationally reconstructed into an image. (c) Two points imaged by classical methods cannot be distinguished from one another if they are too close. The transverse magnification ( ${M_T}$ , magnification of the image field) and the angular magnification ( ${M_A}$ , magnification of the image spot) are equal to each other. (d) The same two points can be distinguished using FINCH imaging because there is less magnification of each spot, though the field size is magnified to the same extent as a standard optical imager focused to this plane such that the image spots do not change from their original position. Adapted from [5].
Fig. 2.
Fig. 2. (I) Optical schematic of original reflected light FINCH layout. (II) Phase-shifted lens patterns (a, b, c; 0°, 120°, 240°) and zoomed section thereof (d) showing the randomly assigned constant phase pixels; (e) magnitude and (f) phase of complex FINCH hologram representing object with three axial planes; (g)–(i) reconstructed images of the three planes created from the complex hologram. Adapted from [4].
Fig. 3.
Fig. 3. (a) Magnitude of the complex hologram of a sample with three fluorescent beads at different axial depths imaged with the first FINCH holographic microscope; (b)–(d) reconstructed images at three axial planes, each containing one bead in focus. Two beads in (b) and (c) are near each other axially but can still be distinguished by the intensities of their peak reconstructed images. The third bead is ca. 50 µm away from the other two but is still reconstructed from the same raw hologram. (e) The axial line profile through a bead comparing wide field (red) to FINCH (blue). Adapted from [7].
Fig. 4.
Fig. 4. Images of USAF test pattern negative, backlit with fluorescence light at Cy3 wavelength, imaged with a ${{20}} \times$ 0.75 NA objective. The FINCH image was recorded with an SLM located between two polarizers as described in the text. The plot shows superresolution in the FINCH image by the significantly increased visibility (contrast) of the smallest features, near the resolution limited size, for progressively varied iris diameters controlling the effective NA of the lens. Smaller objective back aperture is equivalent to reducing the NA of the lens. Adapted from [9].
Fig. 5.
Fig. 5. Images of USAF test pattern negative, backlit with fluorescence light at Cy3 wavelength, imaged with a ${{20}} \times$ 0.75 NA objective on the GRIN-based FINCH system. Note the improved image quality in the FINCH image as compared to the SLM FINCH image in Fig. 4, and similar superresolution as shown by the intensity plots through the smallest features and the visibility (contrast) measurement. Adapted from [12].
Fig. 6.
Fig. 6. (a) Wide-field image and (b)–(d) three reconstructed images of different planes of a fluorescently stained pollen grain sample. In the wide-field image, only one plane of the sample is in focus, but three in-focus planes were reconstructed from the FINCH hologram of a single axial position of the captured sample. Adapted from [12].
Fig. 7.
Fig. 7. Imaging two axial planes of a fluorescent pollen sample with (a), (e) wide field; (b), (f) FINCH; (c), (g) confocal; and (d), (h) CINCH. Adapted from [13].
Fig. 8.
Fig. 8. Schematics depicting the creation and use of a BRL for FINCH imaging. (a) Orientation of the birefringent axes of the crystal in the transverse plane of the lens blank; (b) creation of colinear differentially focused beams by a BRL; (c) use of a long focal length diverging BRL with a shorter focal length standard lens to create a combined BRL system with two overall converging effective focal lengths; (d) side view of a BRL with a compensating birefringent flat (CBF) used to correct for undesired constant phase shift in the BRL. The arrow and dot indicate orthogonal orientation of the ordinary axes of the lens and flat. Adapted from [15].
Fig. 9.
Fig. 9. (a), (c) Wide-field and (b), (d) FINCH imaging of three different stained Golgi proteins in a labeled cell. The superresolving character of the FINCH image is seen in the increased image contrast and better localization of the imaged proteins in their own locations and not overlapped on the other proteins locations. Adapted from [15].
Fig. 10.
Fig. 10. Single-shot BRL FINCH imaging principle. All necessary optical components for single-shot FINCH are shown in this schematic. (a) Polarized image light originating from the object is provided to the BRL. The BRL, which is of high optical quality, splits the incoming image beam into a linearly orthogonally polarized pair of copropagating beams with differing focal lengths. The beams are converted to orthogonal circular polarizations by the QWP and subsequently interfere with one another to create a hologram that is recorded by a camera with multiplexed micropolarizers. Four interspersed phase-shifted holograms are recorded simultaneously. (b) Schematic of the camera pixels overlaid with the interspersed micropolarizer array; the micropolarizer grid has four equally spaced polarizer orientations (0, ${0.5}\pi$ , $\pi$ , and ${1.5}\pi$ rad) precisely arranged on the CMOS die in a repeating square pattern. (c) (i) The recorded hologram is deinterspersed by a computer in one step into four subsampled phases, (ii) then interpolated by nearest neighbor interpolation, (iii) followed by superpositioning to create the complex hologram (iv) before being propagated to create the reconstructed image. Adapted from [5].
Fig. 11.
Fig. 11. Schematic of the FINCH/CINCH microscope. ${{\rm{L}}_O}$ , objective lens; ${{\rm{L}}_1}$ , ${{\rm{L}}_2}$ , relay lenses; D, dichroic mirror to isolate fluorescence excitation from emission light; PBS, polarizing beam splitter; P, S, transmitted and reflected linear polarizations; BRL, birefringent lens; QWP, quarter-wave plate; ${{\rm{L}}_3}$ , standard microscope tube lens. All of the components critical to the FINCH technique are contained in the shaded area. All other components are extrinsic to the FINCH technique and are present only to serve as the basic microscope optics upon which the FINCH system optics is based to create the superresolved image. The FINCH system optics could be added to any microscope optical system. Insertion of the spinning pinhole disk between the ${{\rm{L}}_1}$ , ${{\rm{L}}_2}$ relay lenses converts the system into a confocal FINCH system in which a single image plane is imaged by the FINCH optics (CINCH). With the spinning pinhole disk in place, the standard camera records a confocal image. Adapted from [5].
Fig. 12.
Fig. 12. FINCH lateral resolution of 100 nm subresolution fluorescent beads imaged with a ${{60}} \times$ 1.49 NA Nikon objective at 590 nm emission wavelength significantly exceeds the wide-field resolution of corresponding beads. (a) Wide-field and (b) FINCH images of the identical image field of 100 nm (nominal) beads, with insets showing a magnified detail; (c) plot of two closely spaced beads showing greatly improved two-point resolution with FINCH compared with wide field. The green arrows in (a), (b) point out the bead pair shown in the profiles in this plot. (d) Plot of average bead lateral FWHM made from randomly selected beads; (e) plot of average bead axial FWHM measured by physically stepping the sample through the objective focus over the indicated range in 100 nm steps. Adapted from [5].
Fig. 13.
Fig. 13. (a), (b) Deconvolved confocal and CINCH images of microtubules. Red outlines indicate example comparison areas in which the superresolved CINCH image reveal more detail than is seen in the confocal image. (c) Plots of microtubule lateral FWHM from the deconvolved images. Adapted from [5].
Fig. 14.
Fig. 14. Reflected light FINCH imaging. Original (nondeconvolved) (a) wide-field and (b) FINCH reflected light images of a chrome USAF test pattern printed on a glass slide, taken with a ${{10}} \times$ 0.3 NA objective under 465 nm incoherent illumination. Adapted from [5].
Fig. 15.
Fig. 15. FINCH and comparative wide-field fluorescence imaging (520 nm emission) of the Argolight SIM resolution standard. Images were taken simultaneously using a ${{60}} \times$ 1.49 NA objective and the microscope described in [5]. The plots are taken through the line pair features indicated by the colored lines across the image. The approximate classical Rayleigh limit is indicated on the wide-field plot. The smallest line pair separation (best two-point resolution) achieved with the FINCH image is indicated on the FINCH plot.

Equations (3)

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H θ n ( x h , y h ; z h ) = P ( x h , y h ; R H ) { 2 + e x p { i π λ z r [ ( x h M T x s ) 2 + ( y h M T y s ) 2 + i θ n ] } + e x p { i π λ z r [ ( x h M T x s ) 2 + ( y h M T y s ) 2 i θ n ] } } ,
H F ( x h , y h ; z h ) = a = 1 n H θ a [ e x p ( ± i θ a 1 ± i θ a + 1 ) ] ,
I r e c ( x , y , z r ) = H F ( x , y ; z h ) I R F ( x , y , z r ) .

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