An interferometer with a minimum of optical hardware is employed to measure invasiveness the size of biological samples. Nowadays, there are several techniques in microscopy that render high quality resolved images. For instance, consider optical microscopy that has been around for over a century and has since developed in different configurations such as: bright and dark field, phase contrast, confocal, polarized, and so on. However, only a few of these use interferometry to retrieve not only the sample’s amplitude but also its phase. An interesting example of the latter is digital holography which normally uses a Mach Zehnder interferometer setup. In the research work reported here a transmission digital holographic interferometer designed with a simple and minimal optical hardware, that avoids the drawback of the small field of view present in classical optical microscopic systems, is used to measure the microscopic dimensions of pollen grains. This optical configuration can be manipulated to magnify and project the image of a semitransparent sample over a neutral phase screen. The use of a collimated beam through the sample prevents geometrical distortions for high magnification values. The measurements using this novel configuration have been validated using a standard precision pattern displacement specimen with certified dimensions. As proof of principle, microscopically characterized pollen grains are placed in the transmission set up in order to estimate their dimensions from the interferometrically retrieved optical phase. Results match and thus show a relation between the sample’s size and the optical phase magnitude.
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The possibility to observe the microscopic world awoke centuries ago the natural curiosity of the human kind. From the first microscopic conceptions to date there have been continuous developments to achieve robust, simple and complex optoelectronic microscopic systems. Particularly, optical microscopy has had a rapid and innovative growing in its fundamental principles and techniques thereof, which in all have turned it in a standard tool for the study of a milliard of biological processes on cells and tissues. Nowadays, optical microscopy may be found in the literature and the www with several acronyms and in a variety of techniques. Each one with different capabilities to observe detailed features and processes in cells, as well as exogenous agents acting on them.
High resolution optical microscopy methodologies are divided as surface methods and three dimensional methods . Surface methods include techniques such as near-field scanning optical microscopy (NSOM), total internal reflection fluorescence (TIRF) and surface plasmon resonance (SPR). Three dimensional methods are grouped in non-linear (multiphoton, reversible saturation, second harmonic generation-SHG, two and three photon, and coherent anti-stokes Raman spectroscopy-CARS); deconvolution (stimulated emission depletion microscope-STED, harmonic excitation light microscopy-HELM and others); and confocal and interference methods (Apotome, structure illumination microscopy-SIM, spatial light interference microscopy-SLIM, HELM, 4-PI, image interference microscopy) . Many of the aforementioned techniques share similar backgrounds with a final objective to improve the image quality beyond the diffraction limit. Linked to interferometry, holography has increased its application in microscopy [3–9], viz., digital holographic interferometry (DHI), digital holography (DH) and digital holographic microscopy (DHM), all have been successfully applied for the characterization of tissues and biological samples.
Perhaps the main advantage in using holography is the content of encrypted information within the hologram. On digitally processing holograms it is possible to retrieve the amplitude and phase of the deformed, refracted, reflected, diffracted or deviated wave front coming from the sample; and also back or forward propagate the sample’s wave front. The optical phase is used to measure some physical properties such as deformation, stress, strain and so on . Quantitative phase imaging (QPI) is now an active field of study which quantifies cell induced shifts from the optical path length differences . It was at the end of the last century when DHM proved its usefulness and thus increased its use in the characterization of microscopic biological samples. The dynamic study of live cells has been largely approached and DHM has been actively used in this task [12,13]. Some outstanding research works deal with the recovery of amplitude images of living neurons in culture ; calculate the refractive index and cellular thickness of mouse cortical neuron cultures ; show images of human sperm heads ; reconstruct human red blood cells and pancreas tumor cells ; and found images of mouse embryo fibroblast cells .
DHM creates a non-focused object that appears as being diffracted in the image hologram, an issue that affects the information of an otherwise focused object image . This experimental condition limits DHM applications to only very small samples that deal with its short working distance and limited field of observation (due to the imaging lens) . In this research work an optical system is introduced based in an out of plane digital holographic interferometer set in transmission mode , i.e., the customary optical setup is modified such that micro size samples may be inspected without the DHM drawbacks. Another factor that differentiates our proposed system from a DHM system is that the illumination and sample are not directly located in front of the camera, avoiding possible sensor’s saturation. For this purpose, the object arm is modified to avoid geometrical distortions when the sample under study is magnified. This configuration allows having larger magnification ratios reducing the spherical wave front noise introduced in the microscopic images. The latter avoids the limitations of the working distance and field of view.
The interferometric measurements are validated using a standard precision step displacement specimen with certified dimensions. This validation was also used to prove the cancellation of the spherical wave front contribution in the optical phase maps. As proof of principle biological samples whose size is characterized with a commercial confocal microscope are inspected with the proposed transmission DHI system (t-DHI) to relate the phase information with the data obtained from the confocal microscope. The image processing from both systems (confocal microscope and t-DHI) is presented and described before results are obtained, compared and discussed.
As the optical system is based on a DHI configuration, viz., Fig. 1 (explained in detail in section 3.1), a brief description of its underlying concepts follows. The optical system is a two beam and two object-state optical technique; it uses a reference and an object beam overlapped in one image hologram and thus recorded simultaneously. Two image holograms are required in order to retrieve the optical phase difference, one before (HR) and other after (HO) the object has suffer a displacement. The t-DHI configuration is based on a classical out-of-plane DHI configuration where the camera’s sensor registers the intensity signal of the interference I(x,y), expressed as,22]. Equation (5) renders what is called the wrapped phase map Δφ that hence needs to be unwrapped with an algorithm that results in a smooth optical phase map (Δφ’), i.e., the wrapped map has indeterminate jumps due to the nature of the atan function, situation that is resolved by designing an algorithm that adds 2π to every discontinuity. As t-DHI uses as the object its projection over a neutral phase screen (see Fig. 1), the retrieved optical phase variation cannot be directly related to an object displacement. Instead, it is related with the interaction of the illuminating object beam (which in this setup is a plane wave front) and the object under study. For this reason, the optical phase is normalized to be related to a displacement map (wt) using the next relation:
3. Experimental procedure and results
3.1 Optical set up
The schematic view of the controlled magnification t-DHI system is presented in Fig. 1, where the illumination source is a Verdi laser at 532 nm with an output power of 200 mW. The laser beam is divided in the object (OB) and reference (RB) beams by means of an 80:20 non polarizing beam splitter (BS). Each beam is introduced into a single mode optical fiber using a spatial filter on a mechanical rig. The object beam coming from the output of the optical fiber is expanded, so a lens (CL) is used to collimate it. This collimated beam travels through the sample and then an infinite corrected microscope objective (µObj) expands it toward a neutral phase screen (NPS), thus creating a controlled geometrical magnification of the sample. The NPS is sturdy enough to avoid the introduction of any spurious optical phase variation during the tests .
The magnification variation is obtained with the relative distance between the sample position and the optical fiber output, having a size projection over the NPS with the same microscope objective  as it is shown in Fig. 2(a). However, the new configuration in Fig. 1 avoids the introduction of diffraction effects, removing also the spherical distortion. In the current configuration the variable magnification is also possible by modifying the distance between the microscope objective and the NPS. The latter because the object is now illuminated with a collimated beam and the projection of the microscope objective is fixed. A comparison of these two forms of magnification is shown in Fig. 2(b) and 2(c). Please notice that in Fig. 2(c) a tilting plane profile is more evident than in Fig. 2(b) due to the collimation. The tilting profile is present because the illuminated sample does not have parallel surfaces.
The magnified object’s projection over the NPS is focused on the camera sensor by a lens (L) combined with an aperture (A). The light coming from the reference beam is sent to a 50:50 non polarizing beam combiner (BC) where it directed and further overlapped on the camera sensor with the backscattered light from NPS. This interference pattern is recorded with a sCMOS sensor (PCO EDGE) that has 2560 x 2160 pixels working at a dynamic range of 12 bits. The camera is observing an area over the NPS of 160 x 135 mm.
A precision displacement specimen (model EMD-09000W3) from Federal Products Corporation is used, with a step or height of 5.03 µm and an accuracy of ± 0.127 µm as Fig. 3(a) shows. The standard was placed in the object arm of the t-DHI system and the optical phase map of the pattern is presented in Fig. 3(b). The profile of the optical phase for a linear section (red line in Fig. 3(b)) is presented in Fig. 3(c): it is possible to clearly observe the step, but with the expected speckle noise added. With these results it is possible to validate the measurements and the controlled magnification of the proposed optical system.
3.3 Biological sample
The micro biological samples used are pollen grains from the Lantana flower, selected due to their simplicity to be characterized in a well stablished microscopic technique such as the confocal. Prepared pollen grain samples are commonly used in multi photon microscopy and are clearly imaged in confocal microscopy: this is the reason to use them in this t-DHI system for comparison purposes. It is well known that the pollen is a kind of powder (sum of several pollen grains) produced within the flower’s anthers.
The male reproductive cell, formed by several layers, of the flower is found within each single pollen grain. The intine is the internal layer while the exine is the outer one, the latter being resistant to critical conditions . The Lantana plant grows mainly in American regions with tropical and warm climates so it is possible to find several species [24,25]. It is an easy to adapt plant which hence is considered as invasive to local environments such as different places of Mexico and the United States of America . Figure 4 shows a Lantana flower used to extract the pollen grains for the tests.
To collect the pollen grains a set of microscope glass-slides were used as the first containers. In order to avoid clusters of pollen grains care has to be taken in order to avoid electrostatic conditions during the collection process. An optical microscope (Leica DM3000 LED) was used to observe and evenly distribute several independent pollen grains on the microscope slides. Once the pollen particles were isolated a fixation process was used. As the interferometer works in transmission, several fixation mediums were tested, but many of them distorted the object beam or introduce diffraction patterns as seen on the NPS.
After several tests, the HistoChoice mounting solution (Amresco) was selected. However, in order to avoid a wave front distortion when the solution solidifies, a second slide is placed over the first one, leaving the fixation solution with the pollen grains between them. This arrangement will be referred to as the pollen fixation arrangement (PFA), see Fig. 5.
Several PFAs were made and a control process was designed in order to confirm the solidification of the mounting solution. For this purpose each PFA is situated in the object beam’s path and several image holograms were recorded for a long period of time. By processing these holograms it was confirmed that any optical phase is introduced by motion of the solution. This process also helps as a repeatability test for different PFAs where selected regions are inspected. The PFA’s regions were labeled in order to compare their interferometric signal with the measurements obtained from a Zeiss model LSM 710-NLO confocal microscope. The confocal microscope measures each pollen size of the selected PFA’s regions using a 10X microscope objective in an image with a dimension of 860 x 860 µm. This confocal microscope can generate fluorescence, transmission and compound (sum of the transmission and fluorescence images) images. The resulting confocal measurements are compared with the optical phase information (t-DHI) by means of a homemade algorithm which matches the observed regions between both techniques. Figures 6(a) and 6(b) show the fluorescence confocal microscope image and the t-DHI image (unwrapped phase map) respectively for a sample named PFA_a.
In this PFA_a there are fifteen pollen grains but in the confocal image only eight pollen grains are sharply focused, the others are unfocused (red marks). For this reason, in this sample only the numbered pollen grains were analyzed. Using the confocal image, it is possible to get the dimensions for each pollen grain while the intensity phase value detected with the t-DHI system is registered. From Fig. 6(a), it can be seen that pollen 8 is the largest of all and that pollen grains do not have the same geometry, ergo, some are elliptical, circular, triangular, or some have indeed other irregular forms. Thus, it is necessary to obtain the area of each pollen grain instead of simply its x and y dimensions. The area (confocal microscope) and optical phase intensity (t-DHI) measurements for every pollen grain are calculated and presented as bars in Fig. 7. This information was obtained as follows: a digital image processing algorithm is applied to the confocal image in order to find each pollen’s perimeter. The latter, helps to calculate a pixel area for each one which is finally converted in m2. The optical phase intensity is retrieved by means of the unwrapped phase map, and an algorithm averages a neighborhood around each pollen’s maximum phase value. In this manner it is possible to corroborate that the pollen grain 8 has the larger intensity value and the greater area while the element 7 is the smaller in area and intensity value.
Once the hypothesis of size and phase correlation was confirmed, new PFAs are inspected where different sample conditions are analyzed. Next, samples PFA_b, PFA_c and PFA_d were measured: please observe images from PFA_b with the confocal and t-DHI systems in Fig. 8(a) and Fig. 8(b), respectively.
This PFA shows four different cases of samples’ distribution as described in Table 1:
The confocal transmission image and the processed optical phase map image are shown in Fig. 9. Of particular interest is particle 6: from Fig. 9(a), it results from the addition of two closer pollen grains, where one of them has an irregular form which creates an overlapping in the phase map on the t-DHI image as Fig. 9(b) shows. This intensity value is considerably increased due the sum of the intensities of each pollen grain, a feature shown in Fig. 10.
From Fig. 10 it is possible to observe the two peaks corresponding to each pollen grain of particle 6, with the phase intensity increased over the central part (red arrow). For the rest of the conditions described in Table 1 the optical phase resolves the particle signal smoothly.
Figure 11 shows the area and intensity value for each pollen grain of PFA_b. As expected, if the overlapping factor is omitted particle 6 will appear as the biggest one, but this could be solved by al algorithm to estimate the contribution for each particle in this compound element. In this case, pollen grain 4 is the smaller, both in area and intensity, showing a direct relation between both measurements.
Finally, PFA_d shows two pollen grains that appear very similar in size when observed with the confocal microscope as Fig. 14(a) shows; but they are successfully differentiated by means of the optical phase as Fig. 14(b) shows.
The PFA_d measurements are given in Table 3, where it can be seen that the two pollen grains’ area difference is minimum.
At this point, there is a direct correlation between the size of the micro sample and its optical phase magnitude. However, if a tilt is applied to the PFA when it is placed in the object arm of the interferometer, the phase magnitude is also modified. Three additional tests were performed for PFA_c and PFA_d in addition to the first test, in order to analyze the impact of this tilt. After processing all the information, the phase information in fact does change for each case, but this variation applies to all the observed particles in the PFAs. For this reason, the size classification for each pollen grain remains the same as the one described in Tables 2 and 3.
The t-DHI system with this proposed controlled magnification is a novel optical configuration which could be used to inspect semitransparent biological samples. The system is able to get a smooth phase magnitude which can be related with the dimensions of the sample under study. The validation process of the t-DHI system involved two steps, the first one required a precision displacement specimen while the second was a comparison with confocal images. The latter, proves the ability of the proposed optical configuration to retrieve useful information from semitransparent samples. In this work, the size measurements of the t-DHI system are compared with those of a confocal microscope instead of a DHM system since the phase information has already been validated in  by De la Torre et al. However, this is the first time that this modified version is used to measure biological semitransparent samples, driving to a new spectrum of possible applications that may include the study of inorganic samples.
This work was partially supported by the Consejo Nacional de Ciencia y Tecnología (National Science and Technology Council, CONACYT, Mexico) grant 60136..
All the authors are grateful to Professor Sergio Calixto for his support and access to the calibration displacement pattern.
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