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Abstract
Slightly off-axis digital holographic microscopy (SO-DHM) has recently emerged as a novel experimental arrangement for quantitative phase imaging (QPI). It offers improved capabilities in conventional on-axis and off-axis interferometric configurations. In this contribution, we report on a single-shot SO-DHM approach based on an add-on module adapted to the exit port of a regular microscope. The module employs a beamsplitter (BS) cube interferometer and includes, in addition, a Stokes lens (SL) for astigmatism compensation. Each recorded frame contains two fields of view (FOVs) of the sample, where each FOV is a hologram which is phase shifted by π rads with respect to the other. These two simultaneously recorded holograms are numerically processed, in order to retrieve complex amplitude distribution with enhanced quality. The tradeoff is done in the FOV which becomes penalized as a consequence of the simultaneous recording of the two holograms in a single snapshot. Experimental validation is presented for a wide variety of samples using a regular Olympus BX-60 upright microscope. The proposed approach provides an optimized use of the imaging system, in terms of the space-bandwidth product, in comparison with off-axis configuration; allows the analysis of fast-dynamic events, owing to its single-shot capability when compared with on-axis arrangement; and becomes easily implementable in conventional white-light microscopes for upgrading them into holographic microscopes for QPI.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Corrections
12 March 2019: A correction was made to the funding section.
1. Introduction
Digital holographic microscopy (DHM) combines into a single-platform, high-quality imaging, whole-object wavefront recovery and numerical processing capabilities provided by, respectively, microscopy, holography and computers [1]. As consequence, DHM allows quantitative measurement of the complex amplitude distribution (especially phase information) of the light field that is passing through or is reflected by an inspected sample [2]. For this reason, DHM has becoming in a significant quantitative phase imaging (QPI) technique with strong potential in the bio-field [3–5] where visualization of biosamples using non-invasive (no need to use stains/dyes for contrast enhancement), wide-field (scanning-less technique), real-time (on-line monitoring), non-destructive (no sample damage) and static (no moving components) methods are highly demanded [6–16].
DHM is classically implemented using two opposite interferometric layouts [1]. On one hand, off-axis configuration reintroduces at the recording plane a reference beam which is tilted regarding the imaging beam. This configuration is capable of retrieving whole object wavefront in a single exposure because it is based on the spatial filtering of one of the diffraction orders at the Fourier domain [17]. The single-shot operational principle is really useful for evaluation of, for instance, dynamic processes in live cell imaging while the influence of external vibrations in the measurements becomes minimized. However, the spectral extension of the reconstructed image can be severely limited due to the overlapping between the different diffraction orders at the Fourier domain. For a full separation of the twin imaging terms from the 𝑑𝑐 term at the Fourier domain, it is needed both a carrier frequency equal to at least three times the highest spatial frequency of the object wave and a digital sensor bandwidth at least four times the one of the object wave [18]. Essentially, the pixel characteristics of the digital camera define the relations of the extension and separation of the different diffraction orders [19] which can yield in significant information loss as a consequence of the space-bandwidth product deterioration [20]. On the other hand, on-axis interferometric configuration proposes an in-line geometry where the angle between reference and object beams is set to zero [21]. As a result, the spatial frequency bandwidth of the interferograms becomes narrower in comparison with off-axis modality and on-axis methods provide full optimization of the space–bandwidth product [19] up to a maximum achievable resolution imposed by the camera pixel size for collimated illumination [22]. However, the on-axis scheme needs at least three phase-shifted interferograms that are usually recorded sequentially in time for the complete elimination of the zero order and the twin image terms. Thus, it is not suitable for the analysis of moving samples or dynamic processes.
As a consequence of those pros and cons, a significant number (only a few are included here) of different approaches have been proposed along the past years in order to improve the complex amplitude retrieval in DHM for both off-axis [23–31] and on-axis [32–40] geometries. For instance, off-axis holography has evolved in the sense of improving processing time [25,28] as well as multiplexing different degrees of freedom [29,31]. And on-axis methods have mainly progressed to provide single shot operational principle [32,33,36–38]. In addition, the retrieved phase distribution from the off-axis arrangement has been recently proposed for helping in the in-line phase retrieval algorithm yielding in a hybrid phase retrieval mixed solution for fast, efficient and accurate QPI in DHM [41–44].
Halfway between on-axis and off-axis holographic arrangements, there is a new intermediate implementation mainly developed during the last decade. Instead of full or non-existent overlapping between the different terms at the Fourier domain described in, respectively, on-axis and off-axis layouts, it is possible to define an interferometric configuration allowing overlapping of the DC autocorrelation term with the real/twin image terms but non-overlapping between the two cross-correlation terms. This is easily achieved by controlling the angle between both interferometric beams. Thus, the whole complex amplitude distribution of the object is retrieved by eliminating the central DC term and applying conventional spatial filtering at the Fourier domain [18,24,45]. This arrangement is commonly named as slightly off-axis digital holographic microscopy (SO-DHM) and it proposes an intermediate solution because: i) it only needs two interferograms for phase retrieval, thus optimizing the acquisition rate in comparison with the on-axis layout, and ii) it relaxes the space-bandwidth product requirements of the digital sensor in comparison with off-axis configuration [18,36,46–56]. However, SO-DHM needs two independent measurements of the complex field for removing the DC term allowing access to the complex amplitude distribution of the real image term. Typically, these two images are sequentially recorded in time [18,36,49–55] but single-exposure capability has also been reported by using wavelength multiplexing [46,48], in virtue of the single-shot Hilbert transform operation [47] or with field of view (FOV) multiplexing using a non-polarizing beam splitter (BS) cube [56].
In this manuscript, we present single-shot SO-DHM approach based on a BS interferometric add-on module directly adapted to a conventional white-light microscope that enables to convert it into a holographic one. Single-exposure holographic principle in slightly off-axis geometry is achieved by FOV multiplexing using a BS cube interferometer. Thus, the digital camera records two interferograms in a single-shot that are phase shifted by π rads one to each other. This π rads phase step directly raises when using a BS cube interferometer as background arrangement because the reflected beam at the BS exhibits exactly a phase shift of π rads regarding the transmitted one [57,58]. These two simultaneously recorded SO-DHM holograms are processed using an algorithm based on the subtraction of the two FOVs for eliminating the DC order term [48]. As a result, the spatial frequency distribution of the real image term can be filtered and centered at the Fourier domain and a final inverse digital FT retrieves the complex amplitude distribution of the sample. This algorithm is implemented with the images provided by an add-on module based on a BS interferometer with astigmatism compensating capabilities. The module is compact, robust and it is adapted to the exit port of a regular upright microscope with the added value to convert it into a holographic microscope working in a single illumination shot with low cost components.
2. System analysis
2.1 Layout description
The proposed single-shot SO-DHM approach has been validated using a regular Olympus BX-60 upright microscope. Figure 1 presents a picture of the microscope where the main modifications are depicted for clarity. Essentially, a fiber coupled green diode laser (OSI Laser Diode, TCW RGBS-400R) replaces the white light illumination provided by the mercury lamp of the microscope lamphouse allowing coherent illumination for the holographic recording. Light passes through a linear polarizer (P) to adjust the intensities of both replicas provided by the BS in order to achieve the most similar fringe contrast on both FOVs (this is a critical point in the reconstruction process). The trinocular head of the microscope has been removed just to avoid unwanted spurious reflections, so a tube lens (TL) has been added to maintain the infinity corrected imaging mode. The TL (f’ = 120 mm) is just placed at the circular dovetail mount of the microscope trinocular port.
Fig. 1 Scheme of the proposed add-on module for single-shot SO-DHM in a regular non-holographic microscope. TL – tube lens, M – mirror, SL – Stokes lens, BS – beam splitter, P – linear polarizer, and CMOS – digital camera. A representative raytracing is included showing image duplication for the object ROI.
Then, a labmade add-on module is assembled and mounted at the output port of our modified microscope. It consist of a 45° elliptical mirror (M) mounted into beam steering mirror assembly (Qioptiq) that folds the light path into the horizontal direction towards the Stokes lens (SL), beam splitter (BS) and digital camera (CMOS). Leaving aside the SL (it will be deeply analyzed in next section), the BS (polarizing cube with 25.4 mm side) is placed in a non-conventional way, that is, rotated 45° regarding the position for splitting an incoming beam into two orthogonally separated ones. In this position, it defines a common-path interferometric configuration providing two simultaneous slightly off-axis holograms with a π rad phase step between them [56–61]. This operational principle enables single-shot capability for QPI in SO-DHM at the expense of the FOV reduction. The BS is mounted onto a tilting platform (Qioptiq) including three screws for fine adjustment and alignment. Finally, a CMOS imaging device (Mightex USB3.0 monochrome camera, 2560x1920 pixels, 2.2 μm pixel size, 14 fps) is placed behind the BS for recording of the slightly off-axis holograms. Additional opto-mechanical components (Thorlabs, Linos and Newport) assemble all the components into a single add-on module fixed at the microscope’s output port.
2.2 Astigmatism compensation
The use of a BS in a non-conventional way introduces some aberrations that are critical to be compensated for high quality imaging. In particular, it introduces a non-negligible amount of tilt (prismatic effect) and astigmatism. The tilt effect can be easily compensated by slightly moving the sample at the input plane. But astigmatism compensation needs a more complex device/procedure. Note that, to the best of our knowledge, this is the first time that astigmatism is taken into account in manuscripts involving the use of a BS for interferometric recording since it was not treated before in previous references (only in [59] it is briefly discussed tilt aberration introduced by the BS cube).
The astigmatism introduced by the rotated BS can be easily seen in virtue of the case of a thickness plane-parallel plate that becomes tilted [62,63]. Depending on the illumination vergence, the amount of astigmatism can be significant enough to fully destroy image quality especially the fine sample details. Nevertheless, it can be compensated digitally [64] and with specially designed optical components such as unsymmetrical corrector [62] or variable/adjustable astigmatism compensators [65,66]. We have selected the second option since: i) it is a low-cost device that can be easily implemented at the lab, and ii) it means optical compensation of the astigmatism thus reducing the processing time of the algorithmic stage.
The solution implemented here for astigmatism compensation consists of a SL made by two pure cylindrical lenses of equal but opposite powers which are assembled onto a Risley prism mount. The lenses can be rotated one respect to the other thus varying the resulting astigmatic power from 0 (the axes of the cylindrical lenses are coincident) to the addition in absolute value of the individual cylinders (the axes of the two cylindrical lenses are crossed). And the orientation of the generated astigmatism can be adjusted by global rotation of the whole assembly. Thus, any astigmatism orientation can be optically compensated up to a maximum value of two times the cylindrical power of one of the single lenses integrating the SL. Moreover, the SL does not introduce spherical power since, regardless the orientation of the cylindrical lenses, its mean sphere power is theoretically zero (close to zero due to practical reasons). The SL was proposed by G. G. Stokes in 1849 [67] with the purpose of not to compensate but to measure astigmatism. Nowadays, it is a device used in diary practice for optometric refractive error measurement and it has been applied to different applications such as to improve image quality in eye fundus camera [65], as an adaptive astigmatism-correcting device for eyepieces [66,68], for improving visual acuity measurements [69], and to correct astigmatism at oblique incidence in a wide-angle optical models of the human eye [70].
Figure 2 includes a picture of the labmade SL used in the experiments as well as its experimental characterization using the automatic lensmeter (Topcon CL-300) for power measuring. Since we have used a Risley prism mount for assembling the two cylindrical lenses of powers ± 1.50 D, the relative rotation angle between lenses is determined in prism diopters [outer scale in the Risley prism mount – see Fig. 2(a)]. Nevertheless, it is easy to translate these values into angular degrees following the expression
being θ the rotation angle between the axis of the cylindrical lenses having their axes equally oriented at the beginning, Δ the prism diopters read at the Risley prism mount scale, n the refractive index value of the prisms removed from the mount (n = 1.523) and α the prism apex angle (8 degrees).Fig. 2 SL characterization based on a Risley prism mount: (a) the labmade SL composed by two regular cylindrical lenses of equal but opposite powers ( ± 1.50 D), and (b) the generated cylindrical (black plot), spherical (red plot) and spherical equivalent (blue plot) powers versus relative rotation between lenses. The black/white arrow in (a) represents, respectively, how the angle between lenses and the orientation of the generated astigmatism can be changed.
Thus, calibration of the SL is performed by varying the angle between both lenses, reading the prism diopters at 0.5Δ steps and computing the corresponding values for the rotation angle according to Eq. (1). The angle between lenses is changed by twisting the Risley rotating knob [black arrow in Fig. 2(a)]. Note also as the Risley prism mount has some marks at the outer part corresponding to the angular scale ranging from 0 to 180 degrees at 5 degrees steps. So, it is also possible to identify some control points in the calibration since, for instance, 5Δ and 10.5Δ coincide with 20° and 45°, respectively.
Figure 2(b) shows the values for the spherical (S), the cylindrical (C) and the spherical equivalent (M = S + C/2) components versus the relative angle between cylindrical lenses. We have only considered a relative rotation angle of 90° ( ± 45° per each cylindrical lens) but the curve is symmetrical every 90° [65,66]. As expected, C (black plot) ranges from −3.00 D to 0 D and S (red plot) varies from + 1.50 D to 0 D making M (blue plot) close to 0 D for all the positions (Mmean = 0.03 D). So negligible spherical defocus will be introduced by the SL lens and astigmatism introduced by the rotated BS can be compensated until −3.00 D. Note that higher (or lower) astigmatic power can be generated by selecting cylindrical lenses with higher (or lower) powers.
Just as a proof of concept, Fig. 3 includes an experimental demonstration of the astigmatism influence and its optical compensation by the SL. We have used a resolution test (USAF target) and a 10X/0.30NA microscope lens to illustrate the example. We have only included the central area and not the whole FOV of the images to clearly focus onto the smallest test’s details. When the BS is inserted into the add-on module and rotated around 45° to its working position as BS interferometer, the USAF image is significantly distorted. Figures 3(a) and 3(b) include the aberrated images when, respectively, the vertical and horizontal bars of the resolution test are brought into focus by using the microscope focus adjustment knob. Obviously, the horizontal and vertical bars cannot be resolved due to the presence of the astigmatism. Then the SL is inserted into the add-on module and manually tuned to its best position for astigmatism compensation. The resulting image is included in Fig. 3(c) where no astigmatism aberration is observed. This result is compared against the image provided without the add-on module [Fig. 3(d)] and the central parts magnified for clarity. The main outcome from Fig. 3 is that resolution is preserved since the last resolved element (Group 9 – Element 2) is the same in both astigmatic-free images.
Fig. 3 Astigmatism influence in a BS interferometer: (a) and (b) images obtained after BS inclusion in rotated position where vertical and horizontal bars of the test are focused respectively; (c) image free of astigmatism after the SL is inserted in the add-on module; and (d) direct image without the add-on module for comparison.
2.3 Reconstruction procedure
Using the layout presented in Fig. 1, single-shot SO-DHM can be implemented in a regular non-holographic microscope. Because of the intrinsic characteristic of a BS interferometer, the two single-shot recorded holograms exhibit a phase step difference of π rads [57,58]. So considering that the input FOV is multiplexed into two equal areas, one for the sample and the other for the reference, the output plane recorded distribution will contain two anti-phase shifted holograms in the form of:
being and the auto-correlation/DC terms of, respectively, the object and the reference waves, and and the cross-correlation terms in the form of real and twin imaging terms, respectively. Note as the sign of the auto-correlation terms are opposite between and because of the factors and of the two π rads phase shifted holograms.For the reconstruction process, we have implemented a subtraction algorithm [48] where the DC term can be eliminated by digital computation of the intensity difference in the form of:
Please note that upon subtraction amplitude of two information carrying terms doubled while DC component canceled out. Since we are in slightly off-axis mode (the carrier frequency of the experimental layout can be adjusted by rotating the BS cube in the add-on module), the two retrieved cross-correlation terms are not overlapping between them so the real image term can be filtered out in the Fourier domain making available the complex amplitude distribution of the real image term. However and before computing Eq. (3), fine digital matching of both images from a spatial point of view must be performed in terms of centering of both FOVs that are going to be subtracted. Otherwise, no correct recovery of the sample’s spatial distribution will be performed. This process can be easily implemented using correlation operation of the two FOV halves after astigmatism compensation and before entering the reference beam for the holographic recording. The latter can be easily done by blocking the side corresponding with the reference path of the BS, thus allowing only the transmission of the imaging path.
In order to show the whole reconstruction process and to analyze the advantages of the proposed method, we present the experimental results obtained when a resolution test (NBS 1963A target) is considered as input object. We have moved from USAF to NBS since it contains large clear areas surrounding the resolution elements and this fact is needed for the reference beam transmission as well as to provide a wide area for standard deviation (STD) analysis. Figure 4 includes: Fig. 4(a) the direct image without the add-on module, Fig. 4(b) the distorted image when the BS is introduced, Fig. 4(c) the image free of astigmatism after the SL is inserted, and Fig. 4(d) the recorded hologram when the reference beam is introduced. Insets show 180 lp/mm element for astigmatism compensation and interferometric fringes for clarity.
Fig. 4 Recording sequence in the proposed single-shot SO-DHM method: (a) direct image without the add-on module, (b) astigmatic image generated by the BS, (c) astigmatism-free image using SL, and (d) the single-shot SO recorded hologram.
Then, the proposed reconstruction method is illustrated through Fig. 5 (upper row labelled as 1) in comparison with the results obtained by considering conventional filtering at the Fourier domain (lower row labelled as 2), that is, without computing Eq. (3) and taking only into account one of the two FOVs. For each row, Fig. 5(a) presents the hologram, Fig. 5(b) its Fourier transform, and Fig. 5(c) the filtered spatial-frequency pupil which is used to retrieve Fig. 5(d) the intensity and Fig. 5(f) the phase distributions of the input sample. In addition, Fig. 5(e) includes a plot along the normalized intensity profile of one of the resolution test elements (114 lp/mm) and Fig. 5(g) shows the retrieved phase background image of the clear area marked with a solid line white rectangle in Fig. 5(f). Comparison of Figs. 5(a1)-5(a2) images clearly shows how background is eliminated so the DC term will not take part in the reconstruction process. This fact is made evident also when looking at Figs. 5(b1)-5(b2) and Figs. 5(c1)-5(c2) images since the contribution is readily observable at Figs. 5(b2)-(c2) while avoided at Figs. 5(b1)-(c1). Also, it can be noted that the spectra of real and twin images are separated from each other at Figs. 5(b1)-5(b2) images.
Fig. 5 Comparison results between the proposed system (upper row labelled as 1) and the conventional Fourier filtering method (lower row labelled as 2). Each row includes: (a) the hologram, (b) its Fourier transform, (c) the filtered spatial-frequency pupil, (d) the retrieved intensity image, (e) the plot of the normalized intensity profile marked with the dashed white line in (d), (f) the retrieved phase distribution, and (g) the retrieved phase background image coming from the solid line white rectangle in (f) including the STD value.
The question arises: what will we expect from both reconstructions? Obviously, a noisier and poorer quality image coming from the second row in comparison with the one obtained by the proposed system (first row). This statement is confirmed by plotting the recovered intensity images Figs. 5(d1)-5(d2) through the white dashed lines and by computing the STD values in a background area [white rectangle in Fig. 5(f)] at the retrieved phase images Figs. 5(f1)-5(f2). The plots are included in Figs. 5(e1)-5(e2) and its comparison demonstrates that conventional filtering is mainly noise while the proposed method perfectly identifies the 5 vertical bars as well as the 4 dips coming from the number “114”. And the phase background images are presented in Figs. 5(g1)-5(g2) where the proposed system provides a background smoother than the conventional procedure. This fact is confirmed also by computing the STD value of the images since it is reduced by around 40% (STD values included at Fig. 5).
3. Experimental results on phase samples
3.1 Static biosamples
Our system has been tested with different lines (PC-3, LnCaP and RWPE-1) of prostate cancer cells prepared following the same procedure. The cells were cultured in RPMI 1640 medium with 10% fetal bovine serum, 100U/ml Penincillin and 0.1ug/ml Streptomycine at standard cell culture conditions (37°C in 5% CO2 in a humidified incubator). Once the cells reach a confluent stage, they were released from the culture support and centrifuged. The supernatant fluid is discarded by centrigutation and the cells are resuspended in a cytopreservative solution and mounted in a microscopy slide. Figure 6 shows the experimental results where the different cell lines are placed in different rows. Thus, PC-3 cells are included in the upper row (labelled as 1), LnCaP cells are in the central row (labelled as 2), and RWPE-1 cells are presented in the lower row (labelled as 3). Note that we have not included the whole rectangular FOV retrieved as in Fig. 5 but only a squared area as in Fig. 3 for optimizing the figure artwork.
Fig. 6 Experimental results conducted on static biosamples: upper/central/lower rows are labelled as 1/2/3, respectively, and include PC-3/LnCaP/RWPE-1 cell lines, respectively. Each row includes: (a) the subtraction hologram (I1 – I2), (b) its Fourier transform, (c) the filtered spatial-frequency pupil, (d) the retrieved phase distribution, (e) the 3D plot of the unwrapped phase distribution included in (d), and (f) the same 3D view but considering the conventional Fourier filtering method. Black scale bars in (d) column are 100 μm.
At the different columns, Fig. 6 includes: Fig. 6(a) the subtraction hologram coming from Eq. (3), Fig. 6(b) its Fourier transform without DC term contribution, Fig. 6(c) the filtered pupil at the Fourier domain, Fig. 6(d) the retrieved phase distribution after inverse Fourier transform of the filtered aperture [with spectrum shifting to the center], and Fig. 6(e) the 3D view of the unwrapped phase distribution with quantitative scale bar. In addition, Fig. 6(f) includes the same 3D view but retrieved from conventional Fourier filtering method for comparison with Fig. 6(e). One can notice as noise dominates the retrieved 3D phase profile using conventional tools whereas the proposed system allows perfect visualization of the cells regardless the number of cells in the analyzed FOV (increasing from up to down).
3.2 Dynamic sample
Once SO-DHM was experimentally validated for static biosamples in previous section, our aim here is to demonstrate its validity for real-time measurement of dynamic objects. This is probably the most interesting capability of single-shot SO-DHM. Aimed at this, we have conducted an additional experiment where microbeads (Polybead Microspheres, standard monodisperse polystyrene microspheres) of 90 μm mean diameter are now imaged by a 20X/0.46NA objective lens. The microspheres are flowing in a 100 μm thickness chamber filled with water.
Figure 7 presents the experimental results coming from the proposed system (upper row) and the conventional one (lower row). As in previous figure, Fig. 7(a) includes the hologram, Fig. 7(b) its Fourier transform, Fig. 7(c) the filtered aperture, Fig. 7(d) the retrieved wrapped phase distribution, and Fig. 7(e) the unwrapped phase distribution. Note that it is impossible to retrieve the beads accurate phase information using a single hologram with conventional tools since the DC term overlaps with the twin imaging terms at spectral domain. Thus, the retrieved phase distribution becomes very noisy making impossible a correct phase unwrapping. Hence the single-shot working capability provided by SO-DHM enables accurate QPI analysis of dynamic samples. Moreover, the spectrum at Fig. 7(b1) is perfectly marking the circular coherent aperture of the objective lens for both cross-correlation terms meaning that the DC is efficiently removed (only remains a single central spot probably coming from the auto-correlation term and from general slight imperfections of the subtraction procedure).
Fig. 7 Experimental results for dynamic microbeads: single frame analysis. Results coming from the proposed system are included in the upper row (labelled as 1) and the ones from conventional Fourier filtering method in the lower one (labelled as 2). Each row includes: (a) the hologram, (b) its Fourier transform, (c) the filtered spatial-frequency pupil, (d) the retrieved wrapped phase distribution, and (e) the 2D view of the unwrapped phase distribution included in (d). Black scale bars in (d)-(e) images are 100 μm.
Finishing the single frame analysis, Fig. 8 includes the first frames corresponding with Fig. 8(a) the movie of the recorded set of single shot slightly off-axis holograms (see Visualization 1), Fig. 8(b) the movie representing the subtraction hologram derived from Eq. (3) (see Visualization 2), and Fig. 8(c) the retrieved 3D unwrapped phase profile of the microbeads flowing into the counting chamber (see Visualization 3). We have not included the results incoming from conventional Fourier filtering because, as previously stated, no accurate phase information is retrieved due to phase unwrapping errors.
Fig. 8 Experimental results for dynamic microbeads: movie validation. (a) The recorded set of single-shot SO holograms with FOV multiplexing (see Visualization 1), (b) the movie from the subtraction holograms (see Visualization 2), and (c) the 3D view of the retrieved unwrapped phase distribution by single-shot SO-DHM (see Visualization 3). Black scale bars are 100 μm and insets show interferometric fringes for clarity.
4. Discussion and conclusions
Mainly over the last decade, new and novel simplified, cost-effective, accurate and robust DHM architectures have appeared in the scientific literature [71–85]. Among them, the idea of quantitative coherent sensing with regular microscopes appears as very attractive [71–73,75,78–85]. For instance, SMIM concept [80,83–85] was proposed by our group as a common-path interferometric configuration where minimal modifications are required to convert a regular microscope into a holographic one. The SMIM has been successfully validated considering off-axis holographic recording with Fourier filtering [80], using almost on-axis recording with phase-shifting algorithm [83], with superresolution capabilities to overcome the FOV restriction [84], and in combination with Hilbert-Huang phase microscopy for allowing single-shot operational principle even outside off-axis holographic recording regime [85]. Following in this line, we have presented a new and low-cost way to convert a regular microscope into a holographic one based on FOV multiplexing but with the new insights coming from: i) the use of a BS interferometer, ii) which is implemented under slightly off-axis configuration and iii) integrated into a robust add-on module including optical astigmatism compensation.
On one hand, the use of BS interferometers has been previously reported in the literature [48,56–65] but none of those references deal with the astigmatism introduced when the BS cube is rotated 45° for allowing interferometric replicas. Here, we have deeply analyzed it and proposed an optical compensation strategy based on a SL which is fully integrated into the same add-on interferometric module. According to the relative position of the cylindrical lenses in the SL, we have estimated a total amount of astigmatism equivalent to 0.25 D which is enough for destroying image quality in a microscope, especially at resolution limit (smallest details). Note that the dioptric power (inverse of its focal length) of the TL is 8.33D so the total power of the TL with the astigmatism is 8.58D which means an aberrated focal length of 116.5 mm. This distance is 3.5 mm away from the non-aberrated focal length (120 mm), so the amount of defocus is noticeable.
And on the other hand, SO-DHM has also been proposed as QPI method [18,36,46–56] but single-shot operational principle in SO-DHM is not quite common and requires more complex approaches, such as the use of additional wavelengths [46,48] or the reintroduction of an external reference beam [47], or simply applies to different fields such as lensless microscopy [56]. To the best of our knowledge, this is the first time that single-shot SO-DHM has been implemented in a standard microscope with an external add-on module based on a BS interferometer.
Nowadays, SO-DHM has becoming in an appealed approach for observing dynamic events. The lower the number of recordings, the better the reconstruction in terms of acquisition time and reconstruction errors. The former allows analysis of faster dynamic events ultimately limited by the recording time of a single snapshot. The latter implies that no differences exist between recordings since environmental conditions (thermal/mechanical vibrations, light fluctuations, etc.) are constant in a single snapshot. In that sense, single-shot SO-DHM provides superior performance than classical on-axis interferometry where at least two consecutive holograms are needed. Although parallel phase-shifting DHM has been proposed using different strategies such as modified Hartmann masks [86], micro polarizers attached pixel by pixel to a digital sensor [87], and based on a parallel-quadrature simultaneous phase-shifting method using two identical CCD sensors [88], those techniques are cost-effective from both temporal (computationally demanding) and economically (duplicating some components in the setup). The proposed add-on module is simple, cost-effective and minimally time consuming from an algorithmic point of view.
The experiments included along this paper compare the images retrieved by the proposed single-shot SO-DHM module against conventional Fourier filtering considering a single hologram in slightly off-axis configuration. The comparison shows better performance with improved QPI capabilities when using the proposed technique. Nevertheless, it is possible to increase the carrier frequency in the hologram and move to full off-axis architecture by further rotation of the BS cube. This procedure will recover accurate QPI but it will restrict even more the useful FOV since the central useless area will become enlarged as well as it will endanger the space-bandwidth product of the system. In addition, it is possible to apply a smaller filtering window in the slightly off-axis configuration so the DC term will be prevented in the reconstructed image and better accuracy in QPI will be achieved. However, this procedure will produce resolution limitation as a consequence of the low pass filtering at the Fourier domain, so the reconstruction will be blurred and information will be lost.
Although the proposed method has been validated using an upright microscope configuration, implementation using inverted systems can also be possible and will be a challenge for future works. This possibility will open the door to living cell/tissue culture investigations which are usually performed under inverted microscopes and that have become in a very useful tool in cellular and molecular biology because of their multiple benefits (excellent procedure for studying the normal physiology and biochemistry of cells, the effects of drugs and toxic compounds on the cells, and mutagenesis and carcinogenesis, drug screening and development, and providing a high consistency and reproducibility of the results). Moreover, the use of partially coherence illumination for image quality improvement (coherence noise reduction) can also be a notable field to be explored.
Finally, the proposed method is theoretically valid to any study performed in the field of DHM/QPI provided that the FOV multiplexing will be satisfied. Thus, the only requirement is to defined a special chamber where the sample to be analyzed will be on one side (half FOV) leaving clear/transparent the other half FOV for reference beam transmission. If this condition is accomplished, then the proposed method is theoretically applicable to any DHM/QPI study which is actually carried under conventional DHM/QPI.
In summary, single-shot SO-DHM has been presented and validated into a regular upright microscope by means of a compact, robust and cost-effective add-on module which is directly placed at the microscope’s output port. The add-on module is based on a BS interferometer for the recording of two simultaneous holograms that are shifted π rads one to each other. The add-on module also includes a SL for astigmatism compensation caused by the rotation of the BS. The two holograms are numerically processed for removing the DC term thus allowing the retrieval of the complex amplitude distribution by simple filtering procedure at the Fourier domain. Experiments are reported using different types of samples: resolution test targets are used for calibration and in order to show the whole process step by step, prostate cancer cells show the potential of the method for QPI, and flowing microbeads validate the method for dynamic regime. The main limitations of the proposed method are the FOV reduction as consequence of the spatial multiplexing needed for the recording of the two holograms in a single frame and practical troubles coming from the correct alignment of the added optical elements (mainly SL, BS cube and object illumination) which can yield in poorer quality QPI reconstructions.
Funding
Spanish Ministerio de Economía, Industria y Competitividad and the Fondo Europeo de Desarrollo Regional under the project FIS2017-89748-P and the National Science Center Poland (NCN) (Grant 2017/25/B/ST7/02049) - Statutory Funds Warsaw University of Technology; Polish National Agency for Academic Exchange (PPN/BEK/2018/1/00511).
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