Abstract

Spatial frequency modulated imaging (SPIFI) is a powerful imaging method that when used in conjunction with multiphoton contrast mechanisms has the potential to improve the spatial and temporal scales that can be explored within a single nonlinear optical microscope platform. Here we demonstrate, for the first time to our knowledge, that it is possible to fabricate inexpensive masks using femtosecond laser micromachining that can be readily deployed within the multiphoton microscope architecture to transform the system from a traditional point-scanning system to SPIFI and gain the inherent advantages that follow.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

A. General Introduction

Multi-modal nonlinear spatial frequency modulated imaging (SPIFI) allows an optical microscope to achieve enhanced resolution [1] over fields of view that extend from hundreds of micrometers to millimeters. This enables the user to push boundaries in terms of understanding structure and function, whether it involves biological systems or a platform designed to investigate the physics of a material. The near infrared (NIR) wavelengths (700–1500 nm and beyond) used as the excitation source help optimize penetration depths, an especially significant property when imaging within scattering specimens such as brain tissue [2]. Localization of the multiphoton signal within the focal volume facilitates single-element detection, e.g., with a photomultiplier tube (PMT) or photodiode. This collection method is important for optimizing the image signal-to-noise ratio (SNR) as the signal photons are detected independent of the number or location of scattering events that may occur as they propagate through and exit the specimen on the way to the collection optics.

SPIFI satisfies the important criteria of (1) extended excitation sources for effective acquisition rates, especially important with the ever-increasing demands for a wider field of view; (2) supports single-element detection for image optimization, significant when imaging within a scattering environment; and (3) all the while provides the ability to push the image resolution in multiple linear and nonlinear imaging modalities. To date, SPIFI has been used to image in conjunction with a variety of contrast mechanisms including the fundamental excitation wavelength, second harmonic generation (SHG) and third harmonic generation (THG), and two-photon excitation fluorescence (TPEF) [3,4]. This imaging technique has also been utilized in various other modalities including tomographic imaging [57], fluorescent holographic imaging [8,9], in addition to hyperspectral imaging [10,11].

SPIFI utilizes a cylindrical lens to focus the excitation beam to a line, creating a sheet of light. The light sheet then interacts with a specifically designed mask that modulates the intensity of each resolvable pixel across the light sheet at a different frequency. The modulated line focus is then image relayed (typically with demagnification) to the focal plane of the microscope objective. This results in a projection of time varying spatial frequencies onto the sample [9]. The generated signal light from the desired linear or nonlinear process is collected by an objective lens either in a transmission or epi-detection geometry. All these signal photons are directed to a single-element detector such as a PMT or a photodiode. The resultant voltage versus time signal from the detector can then be Fourier transformed to yield a one-dimensional image. By modulation of the excitation source, in a strategic fashion, we have achieved one-dimensional imaging with single-element detection.

Significantly, Field et al. [1] demonstrated that one of the additional benefits of SPIFI imaging is extended resolution limits. Measurements and modeling demonstrated that for multiphoton imaging modalities in particular, an excitation process that scales as Iη (where I is the excitation intensity and η is the order of the nonlinear process) results in spatial resolution gains up to 2η below the diffraction limit. These results were achieved using a transmissive mask geometry created through lithography. The mask fabrication was performed commercially, with the cost and lead-time for the masks limiting the imaging system optimization process.

The intent of this work is to demonstrate the utility of using femtosecond laser plasma-mediated ablation processes as a method for mask fabrication with several advantages following. The process is in-house, facilitating rapid exploration of mask design and processing techniques. Second, it enables the material and geometry space to be expanded. For example, here we present for the first time to our knowledge both home-built reflective masks in rectangular geometries and transmission masks in polar geometries. Notably, prior to this work, it was not obvious that femtosecond plasma-mediated ablation could be effectively utilized over reflective or transmission surfaces to create a mask with sufficient modulation depth to support the imaging processes described here. The results quantified in this paper, however, show that in fact this is the case, which opens the door to creative, robust mask design with rapid turn around.

B. SPIFI Mask Geometry and Configurations

It is possible to implement the modulation pattern required for SPIFI in rectangular or polar coordinates. This makes the design extremely flexible. Rectangular coordinate masks can be fabricated on reflective substrates and are used when it is desirable to scan the excitation beam across the mask. Polar coordinate masks are desirable for transmission geometries. In this case, the excitation beam is stationary, and is simply transmitted through the mask as it rotates.

Starting by defining the y position in the modulation pattern as

y(t)=νyt,

the modulation equation in rectangular coordinates is described by

m(x,y)=12+12cos(2πΔkrxy),
where x and y are the rectangular coordinates. We define the variable κr as
κr=Δkrνy,
with Δkr being the spatial frequency parameter and νy the velocity in the y direction. It is also beneficial to define the lateral position x relative to the central position xc,
x=x+xc.

The carrier, or central frequency of the modulation, can be defined as

ωc=2πΔkrνyxc,

which when substituting into the original modulation equation in Eq. (2) leads to the new form of the equation,

m(x,t)=12+12cos(ωct+2πκytx).

To convert this continuous modulation equation to binary, the equation can be rewritten as

m(x,t)=12+12sgn(ωct+2πκytx),
where the sgn function is defined to be 1 if the value of its argument is greater than or equal to the desired duty cycle of the mask and 0 if the argument is less than the value of the duty cycle. A key point of the optimized mask design is to realize that the mask diffracts the light sheet as it is reflected or transmitted. Consequently, the duty cycle of the binary mask has a significant impact on the diffracted orders. When describing the duty cycle with the variable Δ,
aj(Δ)=Δsin(πΔj)πΔj
shows which diffracted orders are enhanced and which are suppressed [12]. aj represents the coefficient of the diffracted order number j. The duty cycle chosen for this experiment was 50%, as it suppresses the second and fourth diffracted orders while maintaining a large coefficient in the first diffracted order. A simple visualization of this relationship is shown in Fig. 1.

 figure: Fig. 1.

Fig. 1. Diffracted order coefficient values as a function of the modulation mask duty cycle from Eq. (8). Vertical dashed line represents the 50% duty cycle used in this experiment.

Download Full Size | PPT Slide | PDF

A similar path can be taken to form the angular coordinate version of the modulation equation. By first defining the angular position θ as a function of time by

θ(t)=2πνrt,
where νr is the velocity of the mask at a given radius r, from here it is possible to define the modulation equation in terms of the radial variable ρ and the angular variable θ, or as a function of ρ and time,
m(ρ,θ)=12+12cos(Δkρθ),
m(ρ,t)=12+12cos(2πΔkνrρt).

By following the path for describing the rectangular version of the modulation pattern, we define

κ=Δkνr,
which allows for substitution into Eq. (11) to yield
m(ρ,t)=12+12cos(2πκtρ).

Then, by defining

ρ=x+xckt=2πκtωc=2πκxc
and substituting into Eq. (13), we get
m(x,t)=12+12cos(ωct+ktx).

In the same vein as the rectangular equation, this angular representation can be transformed into binary by rewriting the cosine function as an sgn function,

m(x,t)=12+12sgn(ωct+ktx).

Figure 2 depicts both the continuous and binary versions at 50% duty cycle for the rectangular and angular mask geometries. The binary rectangular mask in Fig. 2(b) was machined for this paper and mounted in place of the spatial light modulator (SLM) normally used to generate the modulation mask pattern in the reflection geometry variant of the SPIFI microscope.

 figure: Fig. 2.

Fig. 2. Sample SPIFI modulation pattern in rectangular and angular coordinates in both (a) and (c) continuous and (b) and (d) binary modulation schemes. Area in a contained in red represents the mask available on a spatial light modulator conventionally used in reflection SPIFI geometries, which has a 1-to-1 aspect ratio.

Download Full Size | PPT Slide | PDF

C. SPIFI Mask Fabrication

1. Laser Machining System

The laser used in the fabrication of the modulation masks is a custom-built KM Labs Zylant Chirped Pulse Amplification (CPA) system [13]. The amplifier produces 180 fs pulses at a 10 kHz repetition rate at a central wavelength of 1040 nm. An Edmund Optics 25.4×12.7mm PFL 90-deg off-axis parabolic aluminum mirror focused 30 mW of average power (delivered to the target) to a 16 μm spot size to fabricate the reflection mask and 137 mW of average power to a 16 μm spot size for the transmission mask. By varying the average power between the two substrates, it is possible to change the actual ablated spot size on the material without modifying the machining system to change the physical beam spot size at the focal plane. The mask substrate is scanned through the focus with Aerotech positioning stages (XY Axis: ANT130-XY Series Two-Axis XY Direct-Drive Nanopositioning Stage; Z Axis: ANT130-L-Z Series Single-Axis Z Direct-Drive Nanopositioning Stage). A program was written in-house to generate the modulation mask pattern and export the necessary G-Code to operate the machining stages.

D. Mask Substrates and Characteristics

A flat protected gold mirror was chosen as the reflective mask substrate because it has a high reflectivity in the near infrared wavelengths used in the microscope system (λ=1040nm) in addition to the substrate being relatively inexpensive ($50) and large enough to fit the entire modulation pattern (25.4 mm diameter, Thorlabs PF10-03-M01). In order to increase the spatial frequency support of the mask, a 2-to-1 aspect ratio was chosen in order to meet minimum Nyquist frequency requirements. The mask was fabricated in air, with a particulate vacuum (BOFA brand) collecting debris during the machining process. The substrate was scanned at a rate of 10 mm/s. After fabrication, the mirror was cleaned with a lens tissue soaked in methanol for additional debris removal.

The transmission mask substrate was a 3-mm-thick, 75-mm-diameter disk made of fused silica. The substrate was scanned at a rate of 10 mm/s. After fabrication, the glass was placed in an ultrasonic bath for additional debris removal. The combination of large area, small feature size (7 μm), and 50% duty cycle significantly increased the fabrication time, and in this case the mask was completed in approximately 20 h. Images of the fabricated modulation masks can be seen in Fig. 3.

E. Amplitude Modulation Capabilities of the Machined Masks

The amplitude modulation capabilities of the two machined masks in the microscopes were experimentally constructed by first removing the cylindrical lens at the entrance of the microscopes to change the line focus on the surface of the mask to a point. In the transmission configuration, the point focus was then scanned in the horizontal direction along the radius of the mask to generate a temporal signal showing a single frequency that varied as a function of position. On the reflection mask, the beam was scanned at different points along the vertical direction to produce a similar collected signal. In both cases, the Fourier transform of the time signal revealed the strength of the reconstructed frequency. This process was repeated across the entire frequency range of the two masks. To illustrate this method, examples of three ideal temporal signals and their locations on both the reflection 4(a) and transmission 4(b) machined masks are shown in Fig. 4. The modulation values of both masks were made under the same imaging conditions employed when taking the data in Figs. 1017.

 figure: Fig. 3.

Fig. 3. Images of the machined SPIFI masks. (a) Image of the transmission mask with (b) a digital zoom in of the same image showing the fine details of the machined channels. (c) Image of the reflection mask with (d) a digital zoom in of the reflection mask image. The two highlighted areas in red show microscope images of the corresponding areas to depict low- and high-resolution feature sizes on the reflective mask.

Download Full Size | PPT Slide | PDF

 figure: Fig. 4.

Fig. 4. Demonstration of how the modulation values of the machined masks were constructed. (a) The machined mask for the reflection geometry microscope, (b) the mask used in the transmission geometry, and (c) shows three simulated example time traces produced by an ideal modulation mask.

Download Full Size | PPT Slide | PDF

In the reflection geometry, the amplitude modulation is accomplished by some portions of the gold substrate being machined away, leaving a scattering glass substrate that would not reflect the beam. In transmission, the modulation is accomplished in a similar manner, wherein the areas free of machining are transparent while the machined areas are heavily scattering. Figure 5 shows three collected temporal modulation signals for the transmission [Figs. 5(a)5(c)] and reflection [Figs. 5(d)5(f)] machined masks. As the frequency increases in the reflection mask geometry, the machined features become smaller than the imaging beam spot size on the mask. This results in aliasing of the modulated signal, which contributes to the decrease in the modulation contrast seen in Fig. 5(f).

 figure: Fig. 5.

Fig. 5. Demonstration of collected frequency data used in calculating the modulation values for the transmission and reflection geometry machined masks. (a)–(c) are three frequency sets for the transmission reticle mask, and (d)–(f) are three frequency sets for the reflection rectangular mask.

Download Full Size | PPT Slide | PDF

Figure 6 shows the reconstructed modulation values for the two machined masks that were collected from the Fourier transform of the single point-scanning technique described previously. Figure 6(a) illustrates the impact of when the laser spot size (15 μm) is mismatched with respect to the mask feature size (5 μm). Not surprisingly, in this case the modulation value decreases with increasing frequency. In Fig. 6(b), the laser spot size and mask features are matched, resulting in uniform modulation.

 figure: Fig. 6.

Fig. 6. Collected intensity modulation of the (a) reflective rectangular machined modulation mask, and (b) the polar transmission mask. Red dots represent the data points reconstructed from the collected signal at each respective frequency.

Download Full Size | PPT Slide | PDF

2. MICROSCOPE CONFIGURATIONS

A. Description of the Microscope Configurations

Two separate microscopes were built to test the performance of the transmissive and reflective machined SPIFI masks. The reflective microscope design is shown in Fig. 7, and the transmissive microscope is shown in Fig. 8.

 figure: Fig. 7.

Fig. 7. Model of the reflection SPIFI microscope layout with the integrated machined modulation mask. Cylindrical lens, CL; polarizing beam splitter, PBS; quarter-wave plate, QWP; scan mirror, SM; scan lens, SL; modulation mask, MM; relay lenses, RL; microscope objective, OBJ; sample location, Sample; collection objective, c-OBJ; photomultiplier tube, PMT; data acquisition card, DAC.

Download Full Size | PPT Slide | PDF

 figure: Fig. 8.

Fig. 8. Model of the transmission SPIFI microscope layout with the integrated machined modulation mask. Cylindrical lens, CL; polarizing beam splitter, PBS; quarter-wave plate, QWP; modulation mask, MM; relay lens, RL; objective lens, OBJ; sample location, Sample; photomultiplier tube, PMT; data acquisition card, DAC.

Download Full Size | PPT Slide | PDF

In the reflection SPIFI microscope the beam enters through a CL (Thorlabs LJ1567L1-B) and is linearly polarized such that it reflects off of the polarizing beam splitter (PBS). The beam is then directed towards the scan mirror (SM) after going through a quarter-wave plate (QWP). The scan mirror (SM) translates the beam across the reflective machined modulation mask (MM) by way of a scan lens (SL) (Thorlabs AC254-100-B-ML). The modulated beam reflects back through the SL, and the polarization of the beam is transformed back to linear after the QWP, which allows the beam to transmit back through the PBS and be image-relayed to the entrance pupil of the microscope objective (OBJ) (Zeiss A-Plan 40×/0.65naPol). Two relay lenses (RL) (2× Thorlabs AC254-200-B-ML) are in a 4-f configuration to accomplish this. After the beam is focused to the Sample, all of the desired signal light is collected by the collection objective (c-OBJ) (COHNA) and transmitted to the PMT. The electronic signal from the PMT is then sent to the data acquisition card (DAC), where the signal is processed to form the final image.

The oscillator used in conjunction with the reflection SPIFI microscope was a ytterbium-doped potassium yttrium tungsten (Yb:KYW) laser with a mode-locked output wavelength of 1040 nm and a pulse duration of 200fs at a repetition rate of 54 MHz. The average power at the input of the microscope was 1.6W, which results in a pulse energy of 29nJ.

The transmission microscope has many of the same components as the reflection configuration. The beam enters through the PBS and is focused onto the machined mask (MM) by the cylindrical lens (CL) (Thorlabs LJ1567L2-B). The mask is image relayed by the RL (Thorlabs LA1050-B) and a QWP to the OBJ (Thorlabs AC508-075-B-ML), where it is focused to the sample. The reflected signal light follows the same path back through the system but has the orthogonal polarization to the input beam because of the double pass through the QWP, so as it reaches the PBS it is reflected and focused onto the photomultiplier tube/photodiode by a lens (L) (Thorlabs AC254-060-B-ML) where the signal is processed by the DAC.

The oscillator used in the transmission microscope was a titanium-doped sapphire (Ti:sapph) laser with a central wavelength of 800 nm and a pulse duration of 85fs at a repetition rate of 76 MHz. The average power at the input of the microscope was 80 mW, which yields a pulse energy of 1nJ.

3. RESULTS AND DISCUSSION

A. Demonstration of Enhanced Resolution

1. Mask Diffraction

In order to examine the diffraction quality and number of diffracted orders produced by the machined modulation mask, images were taken by a camera placed the back focal plane of a lens and compared to images from a traditionally made lithography mask used in previous imaging systems. The mask created via lithography was placed so that the beam was incident on its highest available spatial frequency for the image in Fig. 9(a). The machined mask was then inserted and rotated so that the diffracted pattern matched that of the lithography mask to produce Fig. 9(b). Finally, the machined mask was rotated to its maximum spatial frequency to produce the image in Fig. 9(c).

 figure: Fig. 9.

Fig. 9. Diffracted orders of the machined transmission mask and a printed transmission mask. (a) The maximum diffraction of the printed transmission modulation mask, (b) the a matching diffraction pattern of the machined transmission modulation mask, and (c) the maximum diffraction of the machined transmission modulation mask.

Download Full Size | PPT Slide | PDF

From Fig. 9 it is apparent that the diffraction produced by the machined modulation mask has less overall unwanted structure than the mask created via traditional lithography. Because there is less light put into the unwanted structures on the machined modulation mask, more energy is available to generate the correct signal at the sample. The lithography mask used here was manufactured by Projection Technologies in Dallas, Texas by lithographically printing an aluminum coating onto glass with a resolution of 3600DPI (7μm) [8].

2. Enhanced Resolution Data

The transmission SPIFI setup was used to demonstrate the enhanced resolution capability of the machined modulation masks as in Ref. [1]. The images discussed in this section were formed with the fundamental laser wavelength. Therefore, it should be expected that the higher-order reconstructed image to exhibit twice the resolution of the standard image.

The machined reflection mask was placed at the sample plane as it represents a good analog of a single spatial frequency as a function of position on the mask. The horizontal line focus created by the transmission microscope was placed along the horizontal axis of the reflection mask to facilitate the imaging a single spatial frequency. Full 2D images were made of a portion of the reflective mask, which showed the higher-order image in addition to the standard reconstructed image, and as expected, the higher-order image was twice the width. Figure 10 shows the reconstructed images, where (a) represents the fundamental reconstructed image, (b) the higher-order image, and (c) the higher-order image compressed to the same aspect ratio as the fundamental image with twice the resolution.

Single line images were examined to confirm the fact that twice the pixel density was achieved in the higher-order image. An example is shown in Fig. 11, where the 1D images of the modulation pattern written to the reflective mask were taken from the same position on both reconstructed orders.

 figure: Fig. 10.

Fig. 10. Reconstructed images of the machined reflection SPIFI mask. (a) The fundamental reconstructed image, (b) the higher-order reconstructed image at its appropriate width compared to the fundamental image, and (c) the higher-order image compressed to the aspect ratio shown in (a) that shows the modulation features more clearly.

Download Full Size | PPT Slide | PDF

 figure: Fig. 11.

Fig. 11. Example 1D data from Fig. 10. The blue line represents the 1D image from the fundamental signal, the red line represents 1D image from the higher-order signal, and the cyan and orange points on the corresponding data show the locations of the peaks and troughs used to calculate the value of the enhanced resolution.

Download Full Size | PPT Slide | PDF

Figure 10 also demonstrates the advantage of using the enhanced resolution image when compressed to the correct aspect ratio of the sample, as features barely distinguishable in the fundamental image are made clear with the help of the enhanced resolution.

B. Transmission Mask Images

The images constructed with the transmission mask were of a spot ablated by a CO2 laser operating at 10.6 μm on a copper coated polymer substrate. The image in this section was formed with the transmission microscope shown in Fig. 8 with the polar geometry modulation mask where the fundamental wavelength (800 nm) was used to generate the collected signal. A two-dimensional image is shown as well as selected one-dimensional images to display feature reconstruction.

1. Laser Ablated Spots

The reconstructed images in Figs. 12 and 13 taken post-ablation show a spot that was created via laser ablation on copper coated polymer substrate.

 figure: Fig. 12.

Fig. 12. Reconstructed image of a laser ablated spot on a copper layer deposited on a polymer substrate. The red, blue, and green lines represent the one-dimensional images shown in Fig. 13. The highlighted area is representative of the field of view (FOV) of a 0.25 NA objective which has comparable resolution to the SPIFI system.

Download Full Size | PPT Slide | PDF

 figure: Fig. 13.

Fig. 13. One-dimensional images of the ablated spot shown in Fig. 12.

Download Full Size | PPT Slide | PDF

Figure 13 shows the one-dimensional images of the ablated spot. The red, blue, and green lines represent the 1D images of the ablated spot with the corresponding colors in Fig. 12. From both Figs 12 and 13 it is apparent that the laser ablated spot as well as debris created from the ablation are visible in the reconstructed images.

The transmission microscope design employed for the images in Figs. 913 uses a cylindrical lens with an aperture much larger than the input beam diameter (30 mm versus 14 mm) in conjunction with 50-mm-diameter lenses, which leads to no vignetting in the system. The working distance of the objective lens in this microscope is also large (62.9 mm), which contributes to a large field of view compared to that of a microscope objective with comparable NA. For example, in Fig. 12 we show the field of view of a 0.25 NA microscope objective with a working distance of 10.6 mm. This has implications in the field of laser micromachining as it allows for enhanced resolution with long working distance objectives typically used to modify materials [14].

C. Reflection Mask Images

1. Second Harmonic Generation Images

Lateral images of barium titanate (BaTiO3) particles were formed using the second harmonic signal from the Yb:KYW oscillator. The filters used for the SHG images were Chroma ET510LP, Thorlabs FB520, and BG39 filter glass. The barium titanate particles are 200nm and are below the resolving power of the laser wavelength coupled the 0.65NA objective used in the microscope. With the 0.65 NA objective, the main advantage of using SPIFI was demonstrated, as in the fundamental image of the BaTiO3 there appeared to be a single (BaTiO3) particle. However, the second-order reconstructed image makes the presence of multiple particles apparent. It is important to note that the images shown in Fig. 14, parts (c) and (d) are centered on the fundamental and second order.

 figure: Fig. 14.

Fig. 14. One-dimensional lateral SHG images of BaTiO3 demonstrating higher-order signal reconstruction with a 0.65 NA objective. (a) The traditional NA of a system, (b) the NA of the SPIFI system for the higher-order images, (c) standard resolution image, (d) second-order reconstructed image. The two images show that BaTiO3 particles are resolvable in the higher-order image in contrast to a single mass in the first temporal order.

Download Full Size | PPT Slide | PDF

2. Third Harmonic Generation Images

The third harmonic generation images were conducted with 6 μm polystyrene beads (Polybead polystyrene 6 μm Cat 07312) with UG11 and BG39 filter glasses placed before the detector. An image was made with the 0.65NA that showed higher-order reconstructed image signals similarly to the SHG signal in Fig. 14. The results are shown in Fig. 15.

 figure: Fig. 15.

Fig. 15. 0.65NA images of 6 μm polystyrene beads showing higher-order images exhibiting increased resolution. (a) 2D and (c) 1D fundamental resolution images. (b) 2D and (d) 1D enhanced resolution images.

Download Full Size | PPT Slide | PDF

3. Two Photon Excitation Fluorescence Images

The TPEF images were conducted with 10 μm fluorescent beads (Crimson fluorescent 625/645 63131-4). The filters used for the TPEF images were HQ530 LPM and BG39 filter glass. The fluorescent stained beads were examined to show higher-order image reconstruction is possible in the collected SPIFI signal. An example of how the enhanced resolution images increase the width of the object is shown in Figs. 16(a)16(d).

The raw reconstructed signal showing all four available images is also shown in Fig. 17. If desired, the four one-dimensional images can be compressed to all have the same aspect ratio to reveal enhanced features not visible with the standard resolution image.

 figure: Fig. 16.

Fig. 16. TPEF images of 10 μm fluorescent stained beads. (a) The fundamental image, (b) the second-, (c) the third-, and (d) the fourth-order enhanced resolution images. Horizontal lines show the location of the uncompressed one-dimensional images in (e).

Download Full Size | PPT Slide | PDF

 figure: Fig. 17.

Fig. 17. Raw frequency space data constructed by the Fourier transform of the temporal signal of two 10 μm fluorescent stained beads. The one-dimensional image shows up to a fourth-order frequency signal reconstruction is possible.

Download Full Size | PPT Slide | PDF

4. CONCLUSIONS

A. General Conclusions

SPIFI modulation masks were machined for use in both reflection (rectangular) and transmission (polar) geometries and were shown to be effective in providing the necessary modulation to create images with enhanced resolution in conjunction with the corresponding SPIFI microscopes over fields of view from 100 μm to >3mm. The masks were fabricated with a 50% duty cycle, which optimizes the amount of reflected light in the ±1 diffracted orders of the modulated beam. A limitation of the amplitude modulation technique is that a large portion (50%) of the incident light on the mask is rejected upon reflection or transmission through the substrate. For example, in the case of a 50% duty cycle mask, half of the light is rejected from the system as the beam is modulated.

Higher-order image reconstruction was demonstrated in all nonlinear modalities considered (SHG, THG, and TPEF). The higher-order reconstructed images enable the SPIFI microscope to act as though it has a higher numerical aperture than the fundamental optics provide. In effect, this creates a situation where a high-NA objective is simulated over the field of view of a lower-NA objective. In addition to a larger field of view, a longer working distance is also possible, which makes the system easier to implement within an arbitrary microscope setup. Due to the ultrafast nature of the laser illumination source and the overall microscope design, the demonstrated SPIFI microscopes can facilitate the simultaneous or serial collection of multiple modalities to further increase the information collected from an object.

Funding

Division of Biological Infrastructure (DBI) (1707287); National Science Foundation (NSF).

Acknowledgment

The authors thank Clare Lanaghans for her assistance in imaging the laser ablated spots on copper slides. NeuroNex Technology Hub:Nemonic: Next generation multiphoton imaging consortium. Nathan Worts acknowledges support from MOOG Inc. 500 Jamison RD Plant 20, East Aurora NY 14052.

REFERENCES

1. J. Field, K. Wernsing, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Superresolved multiphoton microscopy with spatial frequency modulated imaging,” Proc. Natl. Acad. Sci. USA 113, 6605–6610 (2016). [CrossRef]  

2. D. Kobat, M. Durst, N. Nishimura, A. Wong, C. Schaffer, and C. Xu, “Deep tissue multiphoton microscopy using longer wavelength excitation,” Opt. Express 17, 13354–13364 (2009). [CrossRef]  

3. M. Young, J. Field, K. Sheetz, R. Bartels, and J. Squier, “A pragmatic guide to multiphoton microscope design,” Adv. Opt. Photon. 7, 276–378 (2015). [CrossRef]  

4. G. Futia, P. Schlup, D. Winters, and R. Bartels, “Spatially-chirped modulation imaging of absorbtion and fluorescent objects on single-element optical detector,” Opt. Express 19, 1626–1640 (2011). [CrossRef]  

5. P. Schlup, G. Futia, and R. Bartels, “Lateral tomographic spatial frequency modulated imaging,” Appl. Phys. Lett. 98, 211115 (2011). [CrossRef]  

6. D. J. Higley, D. W. Winters, G. Futia, and R. Bartels, “Theory of diffraction effects in spatial frequency-modulated imaging,” J. Opt. Soc. Am. A 29, 2579–2590 (2012). [CrossRef]  

7. D. J. Higley, D. W. Winters, G. Futia, and R. A. Bartels, “Two-dimensional spatial-frequency-modulated imaging through parallel acquisition of line images,” Opt. Lett. 38, 1763–1765 (2013). [CrossRef]  

8. J. J. Field, D. G. Winters, and R. Bartels, “Single-pixel fluorescent imaging with temporally labeled illumination patterns,” Optica 3, 971–974 (2016). [CrossRef]  

9. J. J. Field, D. G. Winters, and R. Bartels, “Plane wave analysis of coherent holographic image reconstruction by phase transfer (CHIRPT),” J. Opt. Soc. Am. A 32, 2156–2168 (2015). [CrossRef]  

10. S. R. Domingue, D. G. Winters, and R. Bartels, “Hyperspectral imaging via labeled excitation light and background-free absorption spectroscopy,” Optica 2, 929–932 (2015). [CrossRef]  

11. S. R. Domingue and R. Bartels, “General theoretical treatment of spectral modulation light-labeling spectroscopy,” J. Opt. Soc. Am. B 33, 1216–1224 (2016). [CrossRef]  

12. K. Wernsing, J. Field, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Point spread function engineering with multiphoton SPIFI,” Proc. SPIE 9713, 971304 (2016). [CrossRef]  

13. J. Squier, J. Thomas, E. Block, C. Durfee, and S. Backus, “High average power Yb:CaF2 femtosecond amplifier with integrated simultaneous spatial and temporal focusing for laser material processing,” Appl. Phys. A 114, 209–214 (2014). [CrossRef]  

14. E. Block, M. Young, D. Winters, J. Field, R. Bartels, and J. Squier, “Simultaneous spatial frequency modulation imaging and micromachining with a femtosecond laser,” Opt. Lett. 41, 265–268 (2016). [CrossRef]  

References

  • View by:

  1. J. Field, K. Wernsing, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Superresolved multiphoton microscopy with spatial frequency modulated imaging,” Proc. Natl. Acad. Sci. USA 113, 6605–6610 (2016).
    [Crossref]
  2. D. Kobat, M. Durst, N. Nishimura, A. Wong, C. Schaffer, and C. Xu, “Deep tissue multiphoton microscopy using longer wavelength excitation,” Opt. Express 17, 13354–13364 (2009).
    [Crossref]
  3. M. Young, J. Field, K. Sheetz, R. Bartels, and J. Squier, “A pragmatic guide to multiphoton microscope design,” Adv. Opt. Photon. 7, 276–378 (2015).
    [Crossref]
  4. G. Futia, P. Schlup, D. Winters, and R. Bartels, “Spatially-chirped modulation imaging of absorbtion and fluorescent objects on single-element optical detector,” Opt. Express 19, 1626–1640 (2011).
    [Crossref]
  5. P. Schlup, G. Futia, and R. Bartels, “Lateral tomographic spatial frequency modulated imaging,” Appl. Phys. Lett. 98, 211115 (2011).
    [Crossref]
  6. D. J. Higley, D. W. Winters, G. Futia, and R. Bartels, “Theory of diffraction effects in spatial frequency-modulated imaging,” J. Opt. Soc. Am. A 29, 2579–2590 (2012).
    [Crossref]
  7. D. J. Higley, D. W. Winters, G. Futia, and R. A. Bartels, “Two-dimensional spatial-frequency-modulated imaging through parallel acquisition of line images,” Opt. Lett. 38, 1763–1765 (2013).
    [Crossref]
  8. J. J. Field, D. G. Winters, and R. Bartels, “Single-pixel fluorescent imaging with temporally labeled illumination patterns,” Optica 3, 971–974 (2016).
    [Crossref]
  9. J. J. Field, D. G. Winters, and R. Bartels, “Plane wave analysis of coherent holographic image reconstruction by phase transfer (CHIRPT),” J. Opt. Soc. Am. A 32, 2156–2168 (2015).
    [Crossref]
  10. S. R. Domingue, D. G. Winters, and R. Bartels, “Hyperspectral imaging via labeled excitation light and background-free absorption spectroscopy,” Optica 2, 929–932 (2015).
    [Crossref]
  11. S. R. Domingue and R. Bartels, “General theoretical treatment of spectral modulation light-labeling spectroscopy,” J. Opt. Soc. Am. B 33, 1216–1224 (2016).
    [Crossref]
  12. K. Wernsing, J. Field, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Point spread function engineering with multiphoton SPIFI,” Proc. SPIE 9713, 971304 (2016).
    [Crossref]
  13. J. Squier, J. Thomas, E. Block, C. Durfee, and S. Backus, “High average power Yb:CaF2 femtosecond amplifier with integrated simultaneous spatial and temporal focusing for laser material processing,” Appl. Phys. A 114, 209–214 (2014).
    [Crossref]
  14. E. Block, M. Young, D. Winters, J. Field, R. Bartels, and J. Squier, “Simultaneous spatial frequency modulation imaging and micromachining with a femtosecond laser,” Opt. Lett. 41, 265–268 (2016).
    [Crossref]

2016 (5)

J. Field, K. Wernsing, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Superresolved multiphoton microscopy with spatial frequency modulated imaging,” Proc. Natl. Acad. Sci. USA 113, 6605–6610 (2016).
[Crossref]

J. J. Field, D. G. Winters, and R. Bartels, “Single-pixel fluorescent imaging with temporally labeled illumination patterns,” Optica 3, 971–974 (2016).
[Crossref]

S. R. Domingue and R. Bartels, “General theoretical treatment of spectral modulation light-labeling spectroscopy,” J. Opt. Soc. Am. B 33, 1216–1224 (2016).
[Crossref]

K. Wernsing, J. Field, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Point spread function engineering with multiphoton SPIFI,” Proc. SPIE 9713, 971304 (2016).
[Crossref]

E. Block, M. Young, D. Winters, J. Field, R. Bartels, and J. Squier, “Simultaneous spatial frequency modulation imaging and micromachining with a femtosecond laser,” Opt. Lett. 41, 265–268 (2016).
[Crossref]

2015 (3)

2014 (1)

J. Squier, J. Thomas, E. Block, C. Durfee, and S. Backus, “High average power Yb:CaF2 femtosecond amplifier with integrated simultaneous spatial and temporal focusing for laser material processing,” Appl. Phys. A 114, 209–214 (2014).
[Crossref]

2013 (1)

2012 (1)

2011 (2)

2009 (1)

Allende Motz, A. M.

J. Field, K. Wernsing, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Superresolved multiphoton microscopy with spatial frequency modulated imaging,” Proc. Natl. Acad. Sci. USA 113, 6605–6610 (2016).
[Crossref]

K. Wernsing, J. Field, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Point spread function engineering with multiphoton SPIFI,” Proc. SPIE 9713, 971304 (2016).
[Crossref]

Backus, S.

J. Squier, J. Thomas, E. Block, C. Durfee, and S. Backus, “High average power Yb:CaF2 femtosecond amplifier with integrated simultaneous spatial and temporal focusing for laser material processing,” Appl. Phys. A 114, 209–214 (2014).
[Crossref]

Bartels, R.

E. Block, M. Young, D. Winters, J. Field, R. Bartels, and J. Squier, “Simultaneous spatial frequency modulation imaging and micromachining with a femtosecond laser,” Opt. Lett. 41, 265–268 (2016).
[Crossref]

K. Wernsing, J. Field, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Point spread function engineering with multiphoton SPIFI,” Proc. SPIE 9713, 971304 (2016).
[Crossref]

S. R. Domingue and R. Bartels, “General theoretical treatment of spectral modulation light-labeling spectroscopy,” J. Opt. Soc. Am. B 33, 1216–1224 (2016).
[Crossref]

J. Field, K. Wernsing, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Superresolved multiphoton microscopy with spatial frequency modulated imaging,” Proc. Natl. Acad. Sci. USA 113, 6605–6610 (2016).
[Crossref]

J. J. Field, D. G. Winters, and R. Bartels, “Single-pixel fluorescent imaging with temporally labeled illumination patterns,” Optica 3, 971–974 (2016).
[Crossref]

M. Young, J. Field, K. Sheetz, R. Bartels, and J. Squier, “A pragmatic guide to multiphoton microscope design,” Adv. Opt. Photon. 7, 276–378 (2015).
[Crossref]

J. J. Field, D. G. Winters, and R. Bartels, “Plane wave analysis of coherent holographic image reconstruction by phase transfer (CHIRPT),” J. Opt. Soc. Am. A 32, 2156–2168 (2015).
[Crossref]

S. R. Domingue, D. G. Winters, and R. Bartels, “Hyperspectral imaging via labeled excitation light and background-free absorption spectroscopy,” Optica 2, 929–932 (2015).
[Crossref]

D. J. Higley, D. W. Winters, G. Futia, and R. Bartels, “Theory of diffraction effects in spatial frequency-modulated imaging,” J. Opt. Soc. Am. A 29, 2579–2590 (2012).
[Crossref]

G. Futia, P. Schlup, D. Winters, and R. Bartels, “Spatially-chirped modulation imaging of absorbtion and fluorescent objects on single-element optical detector,” Opt. Express 19, 1626–1640 (2011).
[Crossref]

P. Schlup, G. Futia, and R. Bartels, “Lateral tomographic spatial frequency modulated imaging,” Appl. Phys. Lett. 98, 211115 (2011).
[Crossref]

Bartels, R. A.

Block, E.

E. Block, M. Young, D. Winters, J. Field, R. Bartels, and J. Squier, “Simultaneous spatial frequency modulation imaging and micromachining with a femtosecond laser,” Opt. Lett. 41, 265–268 (2016).
[Crossref]

J. Squier, J. Thomas, E. Block, C. Durfee, and S. Backus, “High average power Yb:CaF2 femtosecond amplifier with integrated simultaneous spatial and temporal focusing for laser material processing,” Appl. Phys. A 114, 209–214 (2014).
[Crossref]

DeLuca, J.

K. Wernsing, J. Field, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Point spread function engineering with multiphoton SPIFI,” Proc. SPIE 9713, 971304 (2016).
[Crossref]

J. Field, K. Wernsing, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Superresolved multiphoton microscopy with spatial frequency modulated imaging,” Proc. Natl. Acad. Sci. USA 113, 6605–6610 (2016).
[Crossref]

DeLuca, K.

J. Field, K. Wernsing, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Superresolved multiphoton microscopy with spatial frequency modulated imaging,” Proc. Natl. Acad. Sci. USA 113, 6605–6610 (2016).
[Crossref]

K. Wernsing, J. Field, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Point spread function engineering with multiphoton SPIFI,” Proc. SPIE 9713, 971304 (2016).
[Crossref]

Domingue, S.

K. Wernsing, J. Field, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Point spread function engineering with multiphoton SPIFI,” Proc. SPIE 9713, 971304 (2016).
[Crossref]

J. Field, K. Wernsing, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Superresolved multiphoton microscopy with spatial frequency modulated imaging,” Proc. Natl. Acad. Sci. USA 113, 6605–6610 (2016).
[Crossref]

Domingue, S. R.

Durfee, C.

J. Squier, J. Thomas, E. Block, C. Durfee, and S. Backus, “High average power Yb:CaF2 femtosecond amplifier with integrated simultaneous spatial and temporal focusing for laser material processing,” Appl. Phys. A 114, 209–214 (2014).
[Crossref]

Durst, M.

Field, J.

J. Field, K. Wernsing, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Superresolved multiphoton microscopy with spatial frequency modulated imaging,” Proc. Natl. Acad. Sci. USA 113, 6605–6610 (2016).
[Crossref]

E. Block, M. Young, D. Winters, J. Field, R. Bartels, and J. Squier, “Simultaneous spatial frequency modulation imaging and micromachining with a femtosecond laser,” Opt. Lett. 41, 265–268 (2016).
[Crossref]

K. Wernsing, J. Field, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Point spread function engineering with multiphoton SPIFI,” Proc. SPIE 9713, 971304 (2016).
[Crossref]

M. Young, J. Field, K. Sheetz, R. Bartels, and J. Squier, “A pragmatic guide to multiphoton microscope design,” Adv. Opt. Photon. 7, 276–378 (2015).
[Crossref]

Field, J. J.

Futia, G.

Higley, D. J.

Kobat, D.

Levi, D.

J. Field, K. Wernsing, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Superresolved multiphoton microscopy with spatial frequency modulated imaging,” Proc. Natl. Acad. Sci. USA 113, 6605–6610 (2016).
[Crossref]

K. Wernsing, J. Field, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Point spread function engineering with multiphoton SPIFI,” Proc. SPIE 9713, 971304 (2016).
[Crossref]

Nishimura, N.

Schaffer, C.

Schlup, P.

Sheetz, K.

Squier, J.

J. Field, K. Wernsing, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Superresolved multiphoton microscopy with spatial frequency modulated imaging,” Proc. Natl. Acad. Sci. USA 113, 6605–6610 (2016).
[Crossref]

K. Wernsing, J. Field, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Point spread function engineering with multiphoton SPIFI,” Proc. SPIE 9713, 971304 (2016).
[Crossref]

E. Block, M. Young, D. Winters, J. Field, R. Bartels, and J. Squier, “Simultaneous spatial frequency modulation imaging and micromachining with a femtosecond laser,” Opt. Lett. 41, 265–268 (2016).
[Crossref]

M. Young, J. Field, K. Sheetz, R. Bartels, and J. Squier, “A pragmatic guide to multiphoton microscope design,” Adv. Opt. Photon. 7, 276–378 (2015).
[Crossref]

J. Squier, J. Thomas, E. Block, C. Durfee, and S. Backus, “High average power Yb:CaF2 femtosecond amplifier with integrated simultaneous spatial and temporal focusing for laser material processing,” Appl. Phys. A 114, 209–214 (2014).
[Crossref]

Thomas, J.

J. Squier, J. Thomas, E. Block, C. Durfee, and S. Backus, “High average power Yb:CaF2 femtosecond amplifier with integrated simultaneous spatial and temporal focusing for laser material processing,” Appl. Phys. A 114, 209–214 (2014).
[Crossref]

Wernsing, K.

K. Wernsing, J. Field, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Point spread function engineering with multiphoton SPIFI,” Proc. SPIE 9713, 971304 (2016).
[Crossref]

J. Field, K. Wernsing, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Superresolved multiphoton microscopy with spatial frequency modulated imaging,” Proc. Natl. Acad. Sci. USA 113, 6605–6610 (2016).
[Crossref]

Winters, D.

Winters, D. G.

Winters, D. W.

Wong, A.

Xu, C.

Young, M.

J. Field, K. Wernsing, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Superresolved multiphoton microscopy with spatial frequency modulated imaging,” Proc. Natl. Acad. Sci. USA 113, 6605–6610 (2016).
[Crossref]

K. Wernsing, J. Field, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Point spread function engineering with multiphoton SPIFI,” Proc. SPIE 9713, 971304 (2016).
[Crossref]

E. Block, M. Young, D. Winters, J. Field, R. Bartels, and J. Squier, “Simultaneous spatial frequency modulation imaging and micromachining with a femtosecond laser,” Opt. Lett. 41, 265–268 (2016).
[Crossref]

M. Young, J. Field, K. Sheetz, R. Bartels, and J. Squier, “A pragmatic guide to multiphoton microscope design,” Adv. Opt. Photon. 7, 276–378 (2015).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Phys. A (1)

J. Squier, J. Thomas, E. Block, C. Durfee, and S. Backus, “High average power Yb:CaF2 femtosecond amplifier with integrated simultaneous spatial and temporal focusing for laser material processing,” Appl. Phys. A 114, 209–214 (2014).
[Crossref]

Appl. Phys. Lett. (1)

P. Schlup, G. Futia, and R. Bartels, “Lateral tomographic spatial frequency modulated imaging,” Appl. Phys. Lett. 98, 211115 (2011).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (1)

Opt. Express (2)

Opt. Lett. (2)

Optica (2)

Proc. Natl. Acad. Sci. USA (1)

J. Field, K. Wernsing, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Superresolved multiphoton microscopy with spatial frequency modulated imaging,” Proc. Natl. Acad. Sci. USA 113, 6605–6610 (2016).
[Crossref]

Proc. SPIE (1)

K. Wernsing, J. Field, S. Domingue, A. M. Allende Motz, K. DeLuca, D. Levi, J. DeLuca, M. Young, J. Squier, and R. Bartels, “Point spread function engineering with multiphoton SPIFI,” Proc. SPIE 9713, 971304 (2016).
[Crossref]

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (17)

Fig. 1.
Fig. 1. Diffracted order coefficient values as a function of the modulation mask duty cycle from Eq. (8). Vertical dashed line represents the 50% duty cycle used in this experiment.
Fig. 2.
Fig. 2. Sample SPIFI modulation pattern in rectangular and angular coordinates in both (a) and (c) continuous and (b) and (d) binary modulation schemes. Area in a contained in red represents the mask available on a spatial light modulator conventionally used in reflection SPIFI geometries, which has a 1-to-1 aspect ratio.
Fig. 3.
Fig. 3. Images of the machined SPIFI masks. (a) Image of the transmission mask with (b) a digital zoom in of the same image showing the fine details of the machined channels. (c) Image of the reflection mask with (d) a digital zoom in of the reflection mask image. The two highlighted areas in red show microscope images of the corresponding areas to depict low- and high-resolution feature sizes on the reflective mask.
Fig. 4.
Fig. 4. Demonstration of how the modulation values of the machined masks were constructed. (a) The machined mask for the reflection geometry microscope, (b) the mask used in the transmission geometry, and (c) shows three simulated example time traces produced by an ideal modulation mask.
Fig. 5.
Fig. 5. Demonstration of collected frequency data used in calculating the modulation values for the transmission and reflection geometry machined masks. (a)–(c) are three frequency sets for the transmission reticle mask, and (d)–(f) are three frequency sets for the reflection rectangular mask.
Fig. 6.
Fig. 6. Collected intensity modulation of the (a) reflective rectangular machined modulation mask, and (b) the polar transmission mask. Red dots represent the data points reconstructed from the collected signal at each respective frequency.
Fig. 7.
Fig. 7. Model of the reflection SPIFI microscope layout with the integrated machined modulation mask. Cylindrical lens, CL; polarizing beam splitter, PBS; quarter-wave plate, QWP; scan mirror, SM; scan lens, SL; modulation mask, MM; relay lenses, RL; microscope objective, OBJ; sample location, Sample; collection objective, c-OBJ; photomultiplier tube, PMT; data acquisition card, DAC.
Fig. 8.
Fig. 8. Model of the transmission SPIFI microscope layout with the integrated machined modulation mask. Cylindrical lens, CL; polarizing beam splitter, PBS; quarter-wave plate, QWP; modulation mask, MM; relay lens, RL; objective lens, OBJ; sample location, Sample; photomultiplier tube, PMT; data acquisition card, DAC.
Fig. 9.
Fig. 9. Diffracted orders of the machined transmission mask and a printed transmission mask. (a) The maximum diffraction of the printed transmission modulation mask, (b) the a matching diffraction pattern of the machined transmission modulation mask, and (c) the maximum diffraction of the machined transmission modulation mask.
Fig. 10.
Fig. 10. Reconstructed images of the machined reflection SPIFI mask. (a) The fundamental reconstructed image, (b) the higher-order reconstructed image at its appropriate width compared to the fundamental image, and (c) the higher-order image compressed to the aspect ratio shown in (a) that shows the modulation features more clearly.
Fig. 11.
Fig. 11. Example 1D data from Fig. 10. The blue line represents the 1D image from the fundamental signal, the red line represents 1D image from the higher-order signal, and the cyan and orange points on the corresponding data show the locations of the peaks and troughs used to calculate the value of the enhanced resolution.
Fig. 12.
Fig. 12. Reconstructed image of a laser ablated spot on a copper layer deposited on a polymer substrate. The red, blue, and green lines represent the one-dimensional images shown in Fig. 13. The highlighted area is representative of the field of view (FOV) of a 0.25 NA objective which has comparable resolution to the SPIFI system.
Fig. 13.
Fig. 13. One-dimensional images of the ablated spot shown in Fig. 12.
Fig. 14.
Fig. 14. One-dimensional lateral SHG images of BaTiO 3 demonstrating higher-order signal reconstruction with a 0.65 NA objective. (a) The traditional NA of a system, (b) the NA of the SPIFI system for the higher-order images, (c) standard resolution image, (d) second-order reconstructed image. The two images show that BaTiO 3 particles are resolvable in the higher-order image in contrast to a single mass in the first temporal order.
Fig. 15.
Fig. 15. 0.65NA images of 6 μm polystyrene beads showing higher-order images exhibiting increased resolution. (a) 2D and (c) 1D fundamental resolution images. (b) 2D and (d) 1D enhanced resolution images.
Fig. 16.
Fig. 16. TPEF images of 10 μm fluorescent stained beads. (a) The fundamental image, (b) the second-, (c) the third-, and (d) the fourth-order enhanced resolution images. Horizontal lines show the location of the uncompressed one-dimensional images in (e).
Fig. 17.
Fig. 17. Raw frequency space data constructed by the Fourier transform of the temporal signal of two 10 μm fluorescent stained beads. The one-dimensional image shows up to a fourth-order frequency signal reconstruction is possible.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

y ( t ) = ν y t ,
m ( x , y ) = 1 2 + 1 2 cos ( 2 π Δ k r x y ) ,
κ r = Δ k r ν y ,
x = x + x c .
ω c = 2 π Δ k r ν y x c ,
m ( x , t ) = 1 2 + 1 2 cos ( ω c t + 2 π κ y t x ) .
m ( x , t ) = 1 2 + 1 2 sgn ( ω c t + 2 π κ y t x ) ,
a j ( Δ ) = Δ sin ( π Δ j ) π Δ j
θ ( t ) = 2 π ν r t ,
m ( ρ , θ ) = 1 2 + 1 2 cos ( Δ k ρ θ ) ,
m ( ρ , t ) = 1 2 + 1 2 cos ( 2 π Δ k ν r ρ t ) .
κ = Δ k ν r ,
m ( ρ , t ) = 1 2 + 1 2 cos ( 2 π κ t ρ ) .
ρ = x + x c k t = 2 π κ t ω c = 2 π κ x c
m ( x , t ) = 1 2 + 1 2 cos ( ω c t + k t x ) .
m ( x , t ) = 1 2 + 1 2 sgn ( ω c t + k t x ) .

Metrics