Digital holographic microscopy of spiropyran‐based dynamic materials

Spiropyran (SP)‐based dynamic materials undergo structural changes in response to external stimuli. In this paper, we show that digital holographic microscopy (DHM) is an effective candidate for characterisation of SPs (embedded in polymer matrices) and for monitoring of their dynamical changes. The polymer matrices are polylactic acid (PLA) and poly(methyl methacrylate) (PMMA) films, which are decorated with SPs and immobilised on graphene quantum dots (GQDs). GQDs are modified by benzylamines prior to the loading of SP species because of the enhancement of hydrophobic characteristics. UV irradiation is used as the external stimulus and the dynamical changes of the samples before and after UV irradiation are measured. DHM is arranged on a novel self‐referencing setup, which substantially reduces the sensitivity of DHM to environmental vibrations. Morphometric information for characterisation of the samples is obtained by analysis of the recorded digital holograms. The experimental results demonstrate the potential of the presented technique to serve as an alternative technique for surface measurement methodologies such as atomic force microscope and stylus profiler for surface characterisation of similar materials.


Introduction
In recent decades, fabrication of dynamic materials using spiropyran (SP) based compounds has been attracted considerable attention.These exclusive compounds undergo structural changes in response to a variety of external stimuli such as temperature, metal ions, pH, and light 1 .A variety of stimuli that can cause reversible changes in these compounds is very wide, which has substantially enhanced the performance of SPs over simple photo-switches.This, in turn, highlights the vast capabilities of new dynamic materials based on SP 2 .Due to the excellent photochromic properties of SP-based compounds, various methods have been developed to construct multipurpose SP-based materials [3][4][5] .From molecular structure view, the ring-closed form of SP molecules may be converted into ring-opened form of merocyanine (MC) through irradiation by UV light which increases the polarity of the molecules [6][7][8] .MCs are in quinoid and zwitterionic states in polar and non-polar environments, respectively.The reversible conversion of MC to SP can also occurs by non-radiative heating.Materials constructed from SPs have been employed in many fields, including reproducible data storage 9,10 , chemical sensing [11][12][13][14] , optical devices 15 , biological imaging 12 , etc., to name a few.SP can be incorporated into different materials, for example biological molecules such as DNA and proteins, mineral particles such as quantum dots (QD), and organic structures such as small organic molecules and polymers.The zwitterionic MC form acts as an energy acceptor to turn off the fluorescence of near energy-matched fluorophores (as an energy donor) 1 .Graphene quantum dots (GQDs) are the example of fluorophores that have many advantages such as fixed fluorescence attributes [16][17][18][19] , high solubility in water 20,21 , and low toxicity [22][23][24][25] compared with traditional semiconductor QDs.One of the most important features of the GQDs are their fluorescence properties 26 and as a novel kind of fluorescent carbon dots they have different applications in optoelectronics, energy-dependent fields, and biology 27 .
In this paper, we examine the transparent polymeric films containing GQDs decorated with SP.Various classes of technologies may be applied for such specimens.Some of them are based on the use of a sharp probe to scan throughout the surface of the specimen in order to collect information about the surface structure 28 .The most common methods in this class include atomic force microscopy (AFM) 29 , Stylus profilometer 30 , and Taylor Hobson profilometer (THP) 31 .AFM can render surface profiles inside a maximum scanning area of about 100 µm×100µm.However, further mapping of larger areas can also be performed with stitching techniques 32 .Stylus profilometer requires force feedback and physically touching the surface, consequently, it is time-consuming and can be destructive to some surfaces.The probe, on the other hand, can also become contaminated by the surface or can be sensitive to some surfaces.THP provides a surface mapping of much larger areas with very high resolution (less than nm) through an elegant integration of interferometric detection with mechanical probing.THP suffers from similar issues of AFM and it is very expensive.The main drawback of the aforementioned techniques, however, is their scanning-based nature, which avoids them to be incorporated for investigation of dynamic phenomena.
Conventional optical microscopy provides imaging of such dynamic phenomena within the Abbe's diffraction limit and works based on the detection of color and intensity of the light passing through the specimen.However, it is not a suitable method for low contrast or phase objects, such as biological samples, as their high transparency avoids adequate contrast required for proper imaging.To increase the contrast, staining the specimens and applying fluorescence microscopy is one of the common approaches.However, relatively high-intensity illumination may change the properties of the samples 33,34 .Instead, phase contrast microscopies and polarimetric microscopy, which use other features of electromagnetic light, i.e., phase and polarization, seems to be useful techniques.Polarimetric microscopy needs multiple snaps to extract information, which makes it unsuitable for dynamic samples.Phase contrast methods, e.g., Zernike's phase contrast microscopy and differential interference contrast microscopy are effective techniques to image phase objects, but these methods are inherently qualitative [35][36][37] .Also, confocal microscopy even if appears to be a suitable candidate, but it is not suitable for dynamic samples [38][39][40] .It is obvious that if one can obtain quantitatively the phase changes throughout the sample it can lead to the 3D information all around the sample.Digital holographic microscopy (DHM), not only provides such task and overcomes the aforementioned shortcomings, but also it can be used for real-time imaging of dynamic samples [41][42][43] .The phenomenon which is considered in this paper, i.e., investigation of polymeric samples and live monitoring of the effect of UV irradiation on them, falls in the DHM-compatible class of phenomena.DHM is a non-contact, non-destructive, and non-scanning technique for quantitative phase imaging, therefore, suitable for retrieving the morphology of biological samples, and surface topography of reflective ones 44 .We have already applied DHM for 3D visualization of myelin figures and their dynamics under thermal gradients 45 , changes in their environmental humidity 46 , studying microstructural surface characterization 47 , evaluation of intergranular corrosion of stainless steel 48,49 , and for 3D characterization of nanocomposites 41 .
In DHM, phase information of an object is preserved through recording the interference between a laser beam passing through the object, so-called "object beam" and a beam from the same laser source, so-called "reference beam", on a digital sensor.The recorded pattern is called "digital hologram", which is subjected to numerical reconstruction and provides the quantitative 3D information about the sample.Even though the technique is a versatile one for numerous applications, but it suffers from the high sensitivity to environmental vibrations and noises.This is caused from the inherent feature of interference phenomena, i.e., the reference and object beams are uncorrelated and a vibration on any of the elements in the optical setup can destroy the interference pattern.Self-referencing DHM (SR-DHM) schemes are smart arrangements to circumvent this disadvantage, and in recent years have attracted an intense attention [50][51][52] .In SR-DHM an object-free-area part of the object beam is taken as the reference beam and is somehow folded onto the rest of the beam, or alternatively, a replica of the object beam is taken as the reference beam and somehow is sheared and overlapped with the object beam.Therefore, the resulted holograms will be vibration-immune, because a single beam is incorporated in the hologram recording and any vibration on the interfering beams is correlated.Moreover, the SR-DHM setups are compact and inexpensive, as they require minimum optical and optomechanical elements.

Results and Discussion
We applied the hologram reconstruction and thickness profile extraction process (See Methods Section, 1.9) to several PLA and PMMA samples, without and with UV irradiation, to achieve statistically reliable ensembles.Figure 1 shows a typical recorded hologram and the reconstructed 2D and 3D images of each case.In Fig. 1(b) the cross-sectional thickness profiles along the line AB, depicted in panel (a) of Fig. 1, are shown.Qualitatively, obvious differences can be seen between the two types of polymers and before and after UV irradiation.However, the main advantage of DHM is its capability to provide quantitative 3D information.Knowing the thickness at each point throughout the sample provides a significant amount of morphological data, from which a comprehensive set of morphometrical parameters may be calculated and used for quantitative assessment of the samples.Depending on the geometry of the sample two classes of parameters may be considered.If the sample is localized somewhere in the field of view, i.e., in the case of a single red blood cell or many other cells, parameters such as volume, projected area, sphericity, eccentricity, and periphery of the cell may be extracted from the DHM reconstruction and are taken as the volumetric parameters to quantitatively classify, distinguish or recognize the samples.On the other hand, if the sample is distributed throughout the field of view, then morphometric parameters such as root mean square (R rms ), skewness (R ske ), and kurtosis (R kur ) are the suitable parameters for quantitative assessments.Nevertheless, in both cases all kind of the parameters can be examined.For the present PLA and PMMA samples, the latter case applies.We define the morphology (or better called roughness) parameters according to ISO-25178-2 standard 56  heights all over the specimens: In these expressions h(m, n) is the height value of mth and nth pixel, M and N are the horizontal and vertical sizes of the reconstructed image, and h(m, n) shows the mean height value.
The roughness parameters can be calculated for any arbitrary ROI of the sample.Here, we consider equal size of ROI and the region center for all the examined samples.R rms , by definition, represents the standard deviation of the distribution, and is a suitable metric to provide a general estimate of the height distribution roughness.It is inferred from examination of the formulas, that a single large peak or valley within the height distribution raises more the roughness parameters of higher moments of the deviation from the mean value.However, due to the presence of third power in R ske it provides a measure for the degree of the symmetry in height distribution roughness about the mean value.A positive R ske shows a "peaky" distribution, while a negative skewness shows the predominance of valleys.R ske =0 indicates a surface with a symmetric heigh distribution.The kurtosis parameter measures the sharpness of the distribution throughout the specimen and is related to the width of the distribution.For an ideally random height distribution, i.e., a Gaussian distribution, R kur equals to 3.0.Smaller kurtosis values show broader height distributions, which corresponds to the specimens with gradually varying, i.e., free of the extreme valley or peak features.On the contrary, the kurtosis values greater than 3.0 demonstrate the presence of deep valleys or inordinately high peaks.It is remarkable that we did not consider waviness parameters, because, in comparison to roughness parameters, they refer to uneven surfaces that appear periodically at longer intervals than the roughness, which is not applicable to our microscopic specimens.We analyze the aforementioned roughness parameters for PLA and PMMA, with and without the UV irradiation.The results are presented as scatterplots of all roughness parameters pairs.The red squares and blue dots represent "with UV" and "without UV" data, respectively.Figures 2(a-c) and 2(d-f) show the scatterplots of for PLA and PMMA polymers, respectively.First of all, the results suggests that the roughness parameters can, collectively, classify the samples.As it can be seen in Figs.2(a-f) exposing both of the polymers to UV irradiation roughens them.In order to quantify the effect, in Figs.2(g-i) we show the average values of R rms , R ske and R kur for PLA and PMMA polymers without and with with UV irradiation, taken over 55 samples in each case along with their corresponding error bars.For both PLA and PMMA all the examined roughness parameters is substantially increased.Moreover, while the UV-induced increase of R rms and R kur for PLA and PMMA are similar, the increase of R ske for PLA is almost twice the increase for PMMA.It shows that the roughness of the samples is more asymmetric, i.e., it includes more numbers of higher peaks.The results are in agreement with the other characterization parameters and may be interpreted as the following.Due to the conversion of SP to MC isomer with high polarity after UV irradiation, the wettability of the films containing Amine-GQDs-SP is increased and the corresponding contact angle is reduced.The most apparent manifestation of polarity switching is the level of change in wetting properties.As a result, the contact angle for PLA-based films is significantly reduced compared to PMMA-based films, due to the more hydrophilic property of PLA compared with PMMA (Figs. 3(a-b) and (f-g)).Moreover, as shown in Figs. to their MC isomeric form.Based on the images recorded from the polymeric films after UV exposure, the appeared color is consistently distributed with considerable intensity throughout the film.Besides, the form of MC is more stable in the PLA/Amine-GQDs-SP film compared with PMMA/Amine-GQDs-SP film due to the hydrophilic property of PLA, which causes the higher color durability and intensity.The above results state that extracting the information of reconstructed digital holograms followed by elaboration of surface roughness parameters may provide an alternative tool for surface characterization in similar cases in which the morphology of the surface is used as a classification criterion.
In conclusion, we suggested the self-referencing digital holographic microscopy (DHM) technique as a useful in situ characterization method for Spiropyran as an important class of dynamic materials.UV radiation is taken as the external stimulus and PLA and PMMA films are considered as polymer matrices.The dynamical changes of the samples before and after UV irradiation are measured quantitatively by volumetric parameters obtained from elaboration of height distribution, which, in turn, are extracted from processing of digital holograms.Especially, roughness parameters are shown as a suitable for sample characterization and classification.Our results collectively show that DHM may be considered as an elegant alternative for in situ evaluation and characterization of dynamic materials and similar ones.

Synthesis of amine-functionalized GQDs
In a round-bottom flask, citric acid (4 g) is added and heated at 200 • C for 15 min.Upon observation of color change of citric acid into light brown, benzylamine (9.33 mmol) is added dropwise during 10 min for amine-functionalization of the GQDs.Finally, the mixture is cooled down to room temperature.The resulting dark brown solid (Amine-GQDs) is washed with adequate water and centrifuged at 6000 rpm for 10 min to remove unreacted material.

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1.3 Synthesis of GQDs decorated with SP Amine-GQDs (200 mg) is mixed with SP (200 mg) and dissolved in THF (10 mL).NHS (0.177 mmol) and DCC (0.566 mmol) are added in the dark and the reaction mixture is refluxed for 30 hours.Then, the reaction mixture is cooled and centrifuged at 6000 rpm.The crimson solution is isolated and the solvent is evaporated.The precipitated material is washed with cold ethanol followed by deionized water for several times to remove unreacted SP, NHS, and other impurities.The obtained solid (Amine-GQDs-SP) is stored in the dark.

Fabrication of polymeric films containing Amine-GQDs-SP
Two polymeric films are fabricated according to the following general procedure.PMMA (0.4 g) is added to DCM (20 mL) and the mixture is stirred toward complete dissolution.Amine-GQDs-SP (10 mg) is added, the polymer solution is stirred for 2 h, and sonicated using an ultrasonic water bath for 15 min.Then, the solution is poured into a petri dish and stored in a dark room.After the complete evaporation of the solvent, the obtained thin film under the name of PMMA/Amine-GQDs-SP is peeled off.For preparation of the second film, PVP (0.05 g) and Amine-GQDs-SP (8 mg) are added to DCM solvent (5 mL) and stirred for a few minutes.Then, PLA (0.95 g) is added to the solution and stirred for 2 h at 25 • C. The prepared homogeneous solution is slowly stirred for 4 h to remove bubbles and the PLA/Amine-GQDs-SP film is prepared according to the aforementioned method.

Contact Angle Measurement
The contact angle of the samples is measured by the sessile drop method 58 .A 7 µl droplet of water is positioned on the film surface.The lateral view image of the drop is captured using a digital camera (Basler, acA2000-165uc, CMV2000, 10 bit) equipped with a C-mount lens of 12 mm fixed focal length.The contact angle is defined as the angle between the baseline of the droplet and the tangent line at the point of contact with the surface.By processing the acquired images in MATLAB c the contact angle is measured.10 droplets of water are used for each polymeric film and their mean contact angle is reported.We measure the contact angle of the films before and after the UV irradiation (wavelength=365 nm) for a duration of 4 min.The calculated values for the contact angles of PLA without and with UV are θ = 55 • ± 2 and θ = 96 • ± 2, respectively.Similarly, the contact angle of PMMA without and with UV are obtained as θ = 64 • ± 1 and θ = 75 • ± 1, respectively Typical images for PLA without and with UV are presented in Figs.3(a-b) and for PMMA in Figs.3(f-g), respectively.

Atomic force microscopy
Figures 3(c) and (h) show the AFM 3D micrographs and the corresponding 2D map of PLA and PMMA polymers without UV irradiation.The AFM experiments are taken by the AFM machine (0101/A, ARA-AFM).

Spectroscopic characterization
UV-Vis/NIR spectrophotometer (Varian Cary 5E UV-Vis-NIR) is employed to record UV-Vis absorption spectra.Fluorescence spectra are recorded by an AvaSpec-128 Starline Ultrafast Fiber-optic Spectrometer.The optical properties of the fabricated films are investigated using solid-state UV-Vis spectroscopy, and a UV lamp at wavelength of 365 nm is employed to study the absorption and visual changes of these compounds.Comparing the fluorescence spectra of Figs.3(d) and (i), the PMMA film shows also a greater and slightly wider fluorescence intensity than the PLA film.As it is clear in Figs.3(e) and (j), after illuminating the sample by UV radiation, a new absorption peak around 575 nm is observed, a finding which is in good agreement with transformation of SP form to the merocyanine (MC) form 13 .By using an excitation wavelength of 400 nm, the fluorescence spectrum from the range of 410 to 750 nm are recorded for two polymeric samples (Figs.3(d) and (i)).The observed peaks around 476 and 627 can be assigned to the spiropyrane and merocyanine forms, respectively 15 .Interestingly, the related peaks for MC form can be improved when the samples are kept under UV irradiation within the aforementioned times.

Experimental procedure
Figure 4 presents the schematic of the novel SR-DHM setup that is used to investigate the samples in this research.The illumination source for DHM is a He-Ne laser (AEO, 632.8 nm, 5 mW) after expansion by the beam expander BE is condensed onto the specimen (S) through the mirror M 1 and by the use of a condenser (C, Thorlabs, CSC2001, Achromatic, NA=0.78,WD=6.6 mm).The microscope objective MO (Olympus, 10×, Plan Achromat, NA=0.25, WD= 10.6 mm) collects the scattered light from the sample (PLA or PMMA polymers).In the presented SR-DHM setup the laser beam diverging from the MO enters into a right-angle prism (Pr).The prism is mounted so that the laser beam hits the edge between the rectangular faces and is divided into two halves passing through the two rectangular faces.Using the mirror M 4 and the beam splitter BS one half is folded onto the other half at the camera.Therefore, a part of the object beam is overlapped withe the rest of it making the required holograms of the sample.In the inset of Fig. 4 the COMSOL software simulation results of the trace of the rays in Pr 6/12 The data acquisition begins before starting the UV irradiation.The dynamics of the polymer specimens are live monitored at 25 fps frame rate.It is remarkable that the presented SR-DHM scheme, which is built on an up-right microscope, can be similarly used on an inverted microscope.Furthermore, the setup has the possibility to be combined with the techniques such as microsphere-assisted microscopy and structure illumination microscopy toward super-resolution DHM 59,60 .A UV light source (Analytik Jena Hand-held UV lamp, 254-365 nm Wavelength, 230 V AC , 60 Hz) along with a collimating lens L (focal length = 10.3 mm) and the steering mirrors M 2 and M 3 are used to provide a uniform UV irradiation on the samples.During the UV light irradiation the DHM laser is blocked by the shutter Sh.

DHM numerical reconstruction
The recoded holograms are subjected to the numerical reconstruction process.When a light-wave is transmitted or reflected from an object its amplitude and phase may be changed and the complex amplitude of the transmitted or reflected light-wave can be expressed as: where, E 0 (x, y) is the amplitude and φ (x, y) is the phase of the light-wave.The numerical reconstruction process in DHM provides quantitatively the full complex amplitude of the sample under study.The recorded digital hologram is the interference pattern of the object and the reference light-waves: 0r (x, y)e iφ s e −iφ r + E * 0s (x, y)E 0r (x, y)e −iφ s e iφ r , where, E 0s and φ s , and E 0r and φ r are the amplitudes and phases of the object and the reference beams, respectively.The numerical reconstruction process includes simulating the illumination of the holograms by the reference beam and the diffraction from the hologram to any specified plane, i.e., free-space propagation into the image formation plane.Usually, the reconstruction based on the scalar diffraction theory suffices in DHM.A number of numerical approaches have been proposed and developed to reconstruct digital holographic images 53 .Amongst, we use the angular spectrum propagation (ASP) method 54 .The ASP method is described in the following.

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The angular spectrum of E s (x, y, z = 0), i.e., the Fourier transform of the recorded hologram, is: where, u and v are the spatial frequencies in x and y directions, respectively.FT denotes the Fourier transform.The spatial frequencies associated with the undiffracted beam, i.e., the first two terms of Eq. ( 6) (also called the zero term), and the virtual image (the third term of Eq. ( 6)) can be simply filtered out in the Fourier domain.The required spatial frequencies, E F s (x, y, z = 0) are then shifted into the center of Fourier domain for further processes, where F denotes filtering.In the Fourier domain we apply a free-space propagation operator to E F s (x, y, z = 0) for a distance of z: λ is the wavelength of the laser beam.Finally, an inverse Fourier transform provides the complex amplitude at z: from which, the reconstructed intensity image, I s , and the phase map, φ s , of the sample are obtained: The intensity image (Eq.9) is similar to a conventional microscope image.However, an important additional feature of DHM over conventional microscopy is "numerical refocusing": it is possible to form the intensity image at any required z plane and if the image is not in-focus, one can apply a different propagation distance to refocus the image.Numerical refocusing is a key feature for DHM-based 3D tracking of multiple objects as it provides the relative distances between out-of-focus objects, quantitatively and at once.On the other hand, the phase is proportional to the optical path length, φ s (x, y) = 2π λ n(x, y)L(x, y), where n is the refractive index and L is the physical length that the light beam passes through.Knowing one of them results in the distribution of the other one.In reflective phase objects, therefore, as the light-wave propagates only in the air (n(x, y) = 1), the phase changes are attributed only to the height variations of the sample surface.For the so-called "phase objects", only φ undergoes a change, which makes DHM as an elegant quantitative methodology for their visualization.
It is remarkable that since the phase is obtained by taking a tangent function, it takes values between − π 2 and π 2 , which creates a discontinuity throughout the phase map.The discontinued phases may be converted into continuous phase maps by "unwrapping procedure".In this research, we use the Goldstein's branch-cut unwrapping algorithm 55 to eliminate the discontinuities.Moreover, we apply linear interpolation operators to get smoother phase maps.In order to remove the effects of the background contaminations and the optical aberrations of setup elements from the final data we record a reference hologram before putting the sample in the experiment.The reconstructed phase of the reference hologram is then subtracted from the other recorded holograms within the reconstruction process.
In Fig. 5 we demonstrate the numerical reconstruction process of a typically recorded digital hologram.The hologram is acquired of PMMA polymer sample after its irradiation by UV. Figure 5(a) shows a typical digital hologram of PMMA polymer sample after its irradiation by UV light.Depending on the sample under investigation the whole digital hologram or a selected region of interest (ROI) may be subjected to reconstruction.In Fig. 5(a) the red square consists the ROI.As explained in Section 3, the hologram (and also the sample-free reference hologram) are Fourier transformed and propagated for a desirable axial distance.In the Fourier spectrum, however, one has the possibility to remove the unwanted spatial frequencies.For example, in Fig. 5(b), 0 and ±1 denote the spatial frequencies associated with the first two DC terms, the third, and the forth terms of Eq. 6, respectively.Only the real image frequencies are kept and shifted into the center of the Fourier space.In the Fourier space, once the propagated complex amplitude is obtained, by using the Eqs. 9 and 10, the intensity image and the phase distribution may be reconstructed.Figure 5(d) is the intensity image.The numerical propagation is done for a distance at which the obtained intensity image is sufficiently sharp.The phase distribution, which, according to Eq. 10, is originally a wrapped phase map (Fig. 5(e)), is subjected to unwrapping process to provide a continuous distribution.Then, the phase map of the reference hologram, which has similarly obtained is subtracted from the sample phase, and data smoothing process is also applied.Finally, from the relationship between the phase, the refractive index, and the thickness, knowing that the refractive index variation during the experimental procedure is negligible, the thickness distribution throughout the ROI is extracted.Figures 5(f

Figure 1 .
Figure 1.Effect of UV irradiation on PLA and PMMA polymers.(a) Digital holograms and 2D reconstructed phase maps of PLA (left) without and (right) with UV irradiation.(b) The cross-sectional profiles along the AB line depicted in panel (a) for PLA (left) without and (right) with UV irradiation.(c) .drawn in 2D maps for without and without UV irradiation Holograms and reconstructed 2D phase maps for without and without UV irradiation; (b) and (e) The cross-sectional profiles along the arbitrary AB line drawn in 2D maps for without and without UV irradiation; (c) The corresponding 3D reconstructed images of PLA (left) without and (right) with UV irradiation.(d-f) Similar reconstruction results for PMMA polymer.

Figure 2 .
Figure 2. The scatterplots of roughness parameters for (a-c) PLA and for (d-f) PMMA polymers.(g-i) The average values of root mean square, skewness and kurtosis for PLA and PMMA polymers without and with with UV irradiation, taken over 55 samples in each case along with their corresponding error bars.

Figure 3 .
Figure 3.The water contact angle measurements of PLA polymer (a) without and (b) with UV irradiation.(c) 3D plot and 2D map of AFM micrographs of PLA polymer without UV irradiation.(d) and (e) Solid phase fluorescence spectra and the UV-Visible absorption, respectively, of PLA polymer film and irradiated UV for exposure times of 20 s, 1min, and 4 min.(f-j) Similar characterization results for PMMA polymer.

Figure 4 .
Figure 4.The schematic of the SR-DHM setup based on the right-angle prism.Sh: shutter, BE: beam expander, C: condenser, S: sample, MO: microscope objective, Pr: prism, L: lens, M: mirror, and BS: beam splitter.Inset: The COMSOL software simulation of the ray trajectories in Pr.
) and (g) show the 2D thickness map and the quantitative 3D image of the ROI indicated in Fig.5(a).

Figure 5 .
Figure 5.The process of numerical reconstruction of digital holograms; (a) A digital hologram of PMMA polymer sample after its irradiation by UV light.The selected region of interest (ROI), denoted by red line is subjected to reconstruction; (b) The Fourier spectrum of the ROI in panel (a).0 and ±1 denote the spatial frequencies associated with the first two DC terms, the third, and the forth terms of Eq. 6, respectively, from which the red dashed line is selected and (c) shifted into the center of the Fourier space; (d) and (e) The reconstructed intensity image (Eq.9) and wrapped phase distribution (Eq.10); (f) and (g) The 2D thickness map and 3D image of the ROI indicated in panel (a), respectively.