Simultaneous dual-wavelength digital holographic microscopy as a tool for the analysis of keratoacanthoma skin samples

A keratoacanthoma (KA) skin tumor is usually caused by sun exposure and may be an alert sign prior to the development of a more aggressive tumor or skin cancer. Studying the shape of the KA cells and their 3D rendering visualization are important parameters to prevent its evolution to higher stages of tumor cells or skin cancer. KA cells shape can be obtained through digital holographic microscopy; for that purpose, a setup with two illumination wavelengths (532 and 638 nm) is implemented to render a synthetic wavelength of 3.2 μm that avoids wrapping the optical phase of the processed holograms and increases measurement range. To recover the optical phase, two off-axis digital holograms are simultaneously recorded at each wavelength. From the processed hologram height variations, the shape and length of KA cells, as well as the stratum corneum epidermal layer, are obtained as phase images. The results achieved aid to discriminate healthy from malignant cells.

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Introduction
Squamous cell carcinoma (SCC) is the second most common type of skin cancer, and it can be preceded by a keratoacanthoma (KA) tumor that grows on the skin.The squamous cell KA skin tumor is a low-grade tumor that starts in hair follicles and has several variants.KA usually presents itself as solitary and can be classified into two types, either as a low-grade squamous cell skin cancer, or as a benign epithelial tumor lesion that can transform into squamous cell cancer [1].The most common risk factor is excessive skin sun exposure, which mainly affects elderly persons; hence, it is important to identify and evaluate solitary KA in its initial stages.In addition to evaluation at the macroscopic level, skin lesions must also be evaluated microscopically.An important parameter is to visualize shape changes in the skin cells, as they may be associated with a particular pathological state.
In the literature, there are several techniques for cell visualization, and many of them are based on optical methods such as digital holographic microscopy (DHM).Holographic microscopic and quantitative phase imaging have proven to be appropriate tools in the field of biomedicine, as in the study of live, dead and fixed cells, just to mention a few applications [2][3][4][5][6][7][8][9][10][11].DHM makes it possible to measure important physical parameters, such as refractive index, volume [12], and shape of cells, among other measurable parameters [13].In this way, it is feasible to correlate information between the healthy or pathological states of the cells.DHM also provides 2D and 3D sample data, since the optical phase and amplitude information embedded in the interferometric patterns can be retrieved [3,14,15].
The DHM with dual-wavelength optical phase unwrapping (OPU) method is used to recover the optical phase images of a wide variety of objects [16][17][18][19].Two, three [20], or more wavelengths can be used to increase the measurement range, which implies the generation of a synthetic wavelength (Λ) [21].This synthetic wavelength is larger than the original wavelengths that generate it, and its value is calculated to be similar to the height variations of the object under study, a variable recorded in the hologram, e.g. of a cell.OPU is based on the principle by which the wrapped phase is related to the height of the object under study and to the wavelength (λ) used; that is, the greater the height of the object compared to λ, the more the phase gets wrapped.A wrapped phase map means that the phase information lies between periodic values in the range [−π, π]; i.e. if the object height is greater than the wavelength, it will be represented in a phase map containing 2π discontinuities.In contrast, when the wavelength used is larger or comparable to the sample height, the optical phase is recovered in an unwrapped fashion with no need to use unwrapping algorithms.A significant advantage is that dual-wavelength OPU provides the unwrapped phase map that avoids the use of phase unwrapping algorithms, and thus avoids the phase unwrapping ambiguity [22].From an unwrapped phase map obtained with dual-wavelength OPU, the acquired phase profiles are associated with the shape and height variations of the sample.This technique has been used either in transmission and reflection DHM configurations and also in different kinds of samples [18,19,23,24].
In what follows, we use a DHM configuration with the dual-wavelength OPU method to simultaneously record two off-axis holograms, in order to obtain data from keratinocytes on some layers of the epidermis taken from skin biopsy specimens that have low-grade squamous cell cancer.From the optical phase embedded in the holograms, the sample's shape, its height variations (related to the phase maps) and the length of the stratum corneum (SC) (the outermost layer of the epidermis) [25,26] as well as the most characteristic signs of the pathology, were obtained [1,27].The method was first validated by using a SiO 2 step with a known thickness of 2 µm, and a refractive index of 1.4760.Compared to other methodologies published elsewhere, viz.[28,29] our research proposal is clearer and easier to implement, making it suitable for the characterization of some features of the keratinocytes.This work's major significance rests in its contribution to the 3D microscopic study of a KA skin cell sample fixed on a coverslip, as well as in a further understanding of its associated pathologies.Individually, measurements were made on the SC, and on keratinocytes of the basal, and spinous layers, locations where the first signs of some of the most common skin cancers occur, e.g., basal and squamous skin cancer.The findings based on optical principles help us to differentiate between samples with and without signs of KA with the potential to be applied in tumor diagnosis.
With the retrieval of 3D shape images displayed in phase maps, it is possible to access point-by-point information on the height of skin cells.In addition, the phase maps of the epidermal layers allow to reproduce the shape of the cells.This is an important biophysical feature to identify the cell type, whether it is malignant or benign.

DHM with dual-wavelength
In a DHM setup, each of the two digital off-axis holograms, for each wavelength, results from the superposition of object and reference waves.As customary, the hologram intensity (I λn (r)) is given by where r = (x,y); ϕ λn (r) is the optical phase information, f 0λn are the spatial carrier frequencies that are introduced in the DHM setup by tilting the beam splitter for each wavelength, λ 1 and λ 2 , respectively, a λn (r) is the background intensity level, b λn (r) is the local contrast function or the fringe modulation function, (n = 1,2) for each wavelength, and * indicates the complex conjugate operator.
The holograms are processed with the angular spectrum algorithm or Fourier transform method to retrieve the ϕ λn (r), yielding [30][31][32] The last two terms of equation ( 2) contain the information of the optical phase within the interference terms of the Fourier spectrum (corresponding to the real and virtual image of the hologram), symmetrically located side by side to a λn (f ).By applying passband filters H c (f 0λn ) at f 0λn frequencies, and performing an inverse Fourier transform, phase information is retrieved: where ϕ λn (r) are the two-wrapped phase maps, ϕ λ1 and ϕ λ2 , of the same object recorded simultaneously at (λ 1 , λ 2 ), and A 0λn is the amplitude of the filtered signal at f 0 λn .In this work, this procedure was applied at each λ for the reference (without sample) and modified state (with sample) holograms, as required for the double exposure technique.
The optical phase recovered from a reconstructed hologram recorded by a DHM setup can be wrapped by a 2π phase modulus, meaning that changes in the optical path are larger than the wavelength used for illumination.One way to resolve such ambiguity is to use a larger wavelength.It can be done using a synthetic wavelength Λ combining two or even multiple wavelengths in a single measurement [16,33,34].The Λ with dual-wavelength is given as, Then, the new synthetic phase map (∆Φ) is produced from ϕ λ1 minus ϕ λ2 .By appropriately choosing the two light sources of wavelengths λ 1 and λ 2 , Λ is increased when the difference between wavelengths decreases.Thus where OPL is the optical path length, n is the refractive index of the object, and h corresponds to the object height variations.In our case, the surrounding medium is air.The synthetic wavelength enables an increase in the range of shape measurements, and thus, it is capable of detecting structures with larger heights.

Experimental setup
Figure 1 shows a transmission DHM configuration using a Mach-Zehnder interferometer optical layout.This system has two laser sources: one at 638 nm, and the other at 532 nm.The beam at 638 nm passes through an acoustic-optical modulator, which provides greater stability to the beam; then, it is filtered and collimated by the spatial filtering stage and The 532 nm laser is guided by beam splitter BS2 and mirrors M3 and M4 towards beam splitter BS3, which splits the light into an object illumination and a reference beam.The object beam (532 nm) is reflected towards the sample through a dichroic filter (DF) that reflects this wavelength and transmits the 632 nm wavelength.The reference beam at 532 nm hits a mirror (M5), and the light reflected from it goes through the microscope objective lens (MO3); then, it is recombined with the object beam at beam splitter (BS4), and finally, is transmitted through beam splitter (BS5) toward the camera sensor.BS4 and BS5 allow control of the incidence angle between the backscattered light from the object and the reference beam, a process that splits the spectral components (frequency shifts at the Fourier space) of the holograms to λ 1 = 532 nm and λ 2 = 638 nm, respectively.
To neglect lens aberrations, microscope objectives MO1 and MO2 are paired, as well as MO3 with MO1; i.e., they have the same magnification and numerical aperture.Lenses MO2 and MO3 compensate the phase curvature produced by MO1 for the beams at 632 nm and 532 nm, respectively.The hologram thus formed is captured with an Allied Vision CMOS Mako U-503B sensor with a resolution of 1944 × 2592 pixels and a pixel size of 2.2 µm; the field of view is 74.8 µm × 96.8 µm.The holographic system's transverse resolution measured in the reconstructed hologram, as well as the transverse scale calibration, were determined with a USAF 1951 resolution test target, and their value was approximately 1.44 µm.
The orientation of the beam splitter BS4 is set at 90 • with reference to beam splitter BS5, enabling the differentiation of the fringes at 532 nm from those at 638 nm in the same hologram.Then, the spectral components for each wavelength are well separated at the Fourier space.
Figure 2(a) depicts the hologram of a test sample recorded simultaneously at dual-wavelength using the experimental setup shown in figure 1.The two intersecting fringe patterns corresponding to λ 1 = 532 nm and λ 2 = 638 nm are shown magnified in figure 2(b); their respective Fourier spectra are observed in figure 2(c) and their corresponding spectral lobules are highlighted with green (532 nm) and red (638 nm) rectangles.

Simultaneously recorded holograms
A total of four samples were analyzed: two with, and two without signs of KA.They were first observed through a commercial Leica optical microscope (DM 2500), and then, the samples were mounted on a motorized stage driven through a control interface, which allows the precise and repetitive location of the areas of interest on the (x, y)-plane; the (x, y) coordinates are stored, which allows returning to different regions of interest without losing the precise location.We identified the SC, the stratum spinosum (SS), and a part of the stratum basale (SB), in addition to the characteristic lobules (keratin pearls) that are present only in samples with signs of KA in the epidermis layer.
Figure 3 shows the flow chart that describes the registration and numerical reconstruction processes of the holograms, selfdescribed in three main stages.

KA sample preparation
The specimen was a skin biopsy from the left hand of a 91 yearold man diagnosed with KA.Initially, the biopsy was studied and diagnosed by an anatomopathologist, and the result was a well-differentiated KA or SCC (squamous cell skin cancer).The pathologist classified the specimens into two groups: with and without KA signs.
The samples were prepared using the standard protocol: fixation, washing out, processing (dehydration, clearing, and embedding), and sectioning [26].To preserve the tissue and the cellular structure of the skin sample, i.e. to harden it as well as protect it from deterioration, it was fixed with formalin.Then, the sample was washed with either water or alcohol to prevent it from hardening excessively.The sample was then dehydrated by means of increasing concentrations of alcohol to remove water from it, and then, clearing is needed because alcohol is not miscible in paraffin (this stage is carried out using Xylol or Toluol, organic solvents, which clean off the alcohol).Next, the samples were embedded in paraffin, which, upon cooling and solidification, provides a support matrix that allows very thin (about 3 mm thick) sections to be taken to a microtome.Finally, very thin cross-sections, 3 µm thick, were made from the hardened block of paraffin to be mounted on slides with acrylic resins as an adhesive.Subsequently, the samples were studied in the DHM setup.

Measurement validation with a SiO 2 step on a coverslip
As proof of concept and validation that the dual-wavelength OPU method works properly for the research presented here, holograms were recorded for a SiO 2 thin film of a known thickness (2 µm) and with a refractive index of 1.4760 [35].The sample of SiO 2 contains a step, and it is deposited on a coverslip.The results of the optical phase maps are presented in figure 4, where the raw wrapped phase maps at (a) 532 nm and (b) 638 nm are shown; (c) shows the raw unwrapped phase map using OPU at 3.2 µm (the synthetic wavelength), along with (d) its profile line obtained after applying a filter is shown detailing the thickness of the step, where the film changes to the reference surface, which is the coverslip.
The thickness or height was determined using equation ( 5), solving for the variable h since the unwrapped phase is obtained by OPU, and the refractive index is known for the step.The good agreement in the thickness results with the real value confirms the correct performance of the dual-wavelength OPU.Where, for the experimental mean value of 1.821 µm, an error of 8.95% was calculated.

Results and discussion
Once the recorded holograms were stored in a computer, a digital reconstruction was carried out and the optical phase was recovered for the SC, SB and SS keratinocytes, as well as for some lobules or keratin pearls, which were only present in samples with signs of KA.
The number of areas identified to recover data was 37 and 22 for the two samples with KA signs, and two for the samples without, respectively.We recorded more than one hologram per area to assure the measurements' repeatability.Fifty holograms were recorded for each area, yielding 1850 holograms registered with KA signs and 1100 without KA signs, thus allowing the averaging of holograms.
From the 37 areas identified in the samples with histopathological signs of KA, in the phase images, we found cells of the SB and SS in 17 regions at 638 nm, and 15 at 532 nm; cells of the SC were also found in 16 regions, and 6 with lobules at 3.2 µm.
Of the 22 areas identified in the samples without KA signs, identification of SB and SS cells was lower, with 6 and 14 regions at 638 nm and 532 nm respectively, and 8 regions of SC at 3.2 µm; no lobules were found.The regions identified are summarized in table 1.
Looking closely at table 1, it is possible to discern between the two types of samples studied, where cells (keratinocytes) in a sample with KA signs showed some ease of identification, mainly at λ = 638 nm.The use of the synthetic wavelength (Λ = 3.2 µm) allows us to identify more cells on the SC, and the main defining factor is the presence of the lobules, which reveal the existence of the KA; hence the relevance of using  the synthetic wavelength to resolve much thicker structures.These findings will be shown next.

Results in samples with KA signs
Figure 5 shows the SC layer for a specimen with KA signs illuminated with a LED source and its corresponding wrapped phase images at wavelengths of 532 and 638 nm.As mentioned, it is possible to apply the dual-wavelength OPU at this point, and the SC layer is a perfect candidate to be resolved with it.The resulting unwrapped phase is shown in figure 6 Figure 6 shows the results of the unwrapped phase with dual-wavelength OPU, corresponding to the same SC layer, which was shown in wrapped phase images in figures 5(b) and (c).In order to show details in some areas of the SC, transverse regions of the unwrapped phase (red, blue, and green colored lines) are selected to retrieve their corresponding line profiles, plotted on the right of figure 6.These phase profiles are related to the sample height variation (in radians) since it can be used to identify SC from a sample with KA signs.
Figures 7(a) and (c) show sample regions identified with Keratinocytes from SB and SS cells in a sample with KA signs illuminated with a LED.Figures 7(b) and (d) show the unwrapped phase maps of the keratinocytes retrieved directly at 638 nm and 532 nm respectively.Particularly, notice in figure 7(b) the full region unwrapping using 638 nm: the cells' height variations (i.e., in phase profiles) shown are around this wavelength value.But in figure 7(d), some remnant wrapped regions can also be observed meaning greater height variation than the 532 nm wavelength.In general, SB and SS in a sample with KA phase maps are within a range of less than 2π; therefore, they do not need the dual-wavelength OPU or any phase unwrapping algorithms, and then, visualizing them is straightforward.
As it may have been expected, it can also be seen that the shape of the cells is not homogeneous, which may also indicate that cells in the spinous and basal layers are being observed.This is due to the shapes identified in the images: oval and small for the basal layer, and slightly rounder and larger for the SS layer, in addition to the differentiation of the characteristic spines in this layer (white spacing with some gray fringes between cells).Regarding the stratum granulosum (SG), no cells could be differentiated in this layer; according to some authors, SG is not present in all parts of the skin [36].
The measurements made in these phase images correspond to both height variations (given in radians) and diameters in the case of cells with circular shapes, or minor and major semiaxes in those with elliptical shapes [37].For descriptive purposes, some of the cells on the phase images were labeled with numbers and colors to graphically indicate their corresponding sizes along the color lines and height variation profiles (to the right of each image).The variation of the latter might be due to the presence of the KA signs that causes changes in the cell's shape (i.e., phase maps).Figures 7(e) and (f) show a 3D mesh plot for some (chosen at random) of these cells.A significant finding was the characteristic lobules of KA, shown in figure 8.In these regions, keratinocytes' growth is around a central point; these configurations are also called keratin pearls.Three lobules can be seen in figure 8(a): one at the bottom, one at the center, and one to the left, labeled with numbers 1, 2, and 3, respectively.Figures 8(b) and (c) show wrapped phase maps, which were also used to apply the dual-wavelength OPU whose results are shown in figures 8(d) and (e).As seen before, on the right side of these unwrapped phase maps, some values of their transverse phase profiles and lengths are measured.
Figure 8(e) presents the phase information for lobule 2 obtained with dual-wavelength OPU.From this, the height variation is measured in radians, where its maximum value is 3.8 rad, and likewise, its transverse length is determined in µm, resulting in an average length of 19.51 µm.The height of this lobule is greater in comparison to the maximum value measured in individual SB and SS keratinocytes, another distinguishing result in samples with KA signs.

Results in samples without KA signs
A repetitive and common result in samples with KA signs was the clear differentiation of keratinocytes, an issue that was not easily achieved in samples without KA signs.When the sample was illuminated by the LED source and lasers, the keratinocytes were more difficult to observe (see figure 9).Even so, for the samples without KA signs, the unwrapped phase of keratinocytes at 532 nm was more easily recovered than that at 638 nm, which, in comparison with figure 7(d), may indicate that the height variation of the cells in these samples could be less than in those with KA signs.No lobules were detected in samples with no KA, whereas they were identified in samples with KA signs.
Table 2 summarizes the findings for the cells with and without KA signs.It is readily noticed that the average and the average of the maximum height values for the cells in SS and SB with KA signs are higher than those for cells without KA signs.The opposite is true for the length measurements: the greater the height, the shorter the length, and vice versa.These results were quantified for 532 and 638 nm.Also, the results suggest that the keratinocytes cells in samples with KA signs may be related to cutaneous SCC pathology, a situation due to cytoplasmic swelling [38].This peculiar characteristic allows one to identify and correlate the cell samples with a pathological state.
Another distinctive point to discriminate between samples with and without KA signs are the results in the SC, where the height is smaller in this layer and its length is larger with KA as compared to samples without KA signs.Notice that these results were obtained using the synthetic wavelength.The results with the SC length are in agreement with those in [26] regarding the SCC pathology: the SC layer tends to be thicker (in 2D using classical optical microscopy), meaning longer lengths in the results (which is also employed as a characteristic to correlate a pathologic state with the sample).A definite fact is the presence of lobules found uniquely at the synthetic wavelength in malignant specimens.
Additionally, table 2 shows the average, standard deviations (SD) and maximum height, and length from the phase maps in samples with and without KA signs at 532 nm, 638 nm, and Λ at 3.2 µm.The dual-wavelength DHM technique was used to assess the thickness/height and length of epidermal layers and cells, to the best of our knowledge, they have not been applied to this type of samples, nor with the preparation protocol did they receive.Compared with other works where the same technique was used, the contributions were generally on cell lines.
In figure 10, the plots show the number of measurements, as a function of the height-measured values and length, performed on the lobules present in the samples with KA signs.The plots help to visualize the changes between characteristic lobules in the samples with KA signs, as well as the relevance of the results shown.It is identified that the values obtained for the maximum and average height exceed the same parameters in the individual cells (SS and SB) of samples without and with KA signs; a similar behavior was identified in the length measurements.It is worth mentioning that the values obtained for these parameters maintain the same behavior; i.e., they are independently related to the number of measurements.This was an expected result, once the lobules or keratin pearls are indeed formations of more than one keratinocyte; nevertheless, to the best of our knowledge, no 3D characterization of these lobules exists.

Conclusions
The dual-wavelength OPU method was implemented in a DHM configuration employing simultaneously two wavelengths, λ 1 = 532 nm and λ 2 = 638 nm to record the holograms.The potential of the technique was demonstrated by making measurements on skin cell samples and correlating them with their pathological state, since its evaluation is very important to prevent the development of a more aggressive tumor or skin cancer.Consequently, the optical phase information from skin samples of a patient previously diagnosed with KA was recovered without the need to apply the most commonly used phase unwrapping algorithms, a process that has proved to be time-consuming and rather cumbersome in some cases.The procedure used avoids the OPU ambiguity and increases the measurement range.With the optical phase information, the length of the cells and the height variation shown as phase profiles with their corresponding statistics were obtained as parameters used to assess the presence or absence of signs of the mentioned pathology in the samples.The layers of the epidermis, the SC, the keratinocytes in the SB and SS layers with and without KA signs, and their respective shapes in 2D and 3D in the form of unwrapped phase maps, were identified.The synthetic wavelength (Λ) allowed for the measurement of epidermal information such as SC and lobes (keratin pearls) with no need of unwrapping algorithms as needed in techniques where only a single wavelength is used.Compared to previous dual-wavelength digital holographic microscopes, our setup was used to evaluate the thicknesses of epidermal layers and cells; to the best of our knowledge, this type of microscopy has not been applied to this type of sample, neither with the preparation protocol that they received.
The results of the measurements showed a correlation between the presence or absence of KA signs, where a greater height for the cells of the SS and SB layers was found in the samples with KA signs, while in the cells of the KA-free samples, this behavior was the opposite.With these values, it seems that the cells of these layers of the samples with KA undergo a swelling process.Another differentiating factor was the measurements made on the SC: its length was greater in the samples with KA signs, and vice versa in the samples without them.
Validation of the results obtained on KA samples was successfully tested by applying the dual-wavelength OPU on a SiO 2 thin step with known thickness and refractive index.These results could allow our methodology to also be used for other types of tissues and cells with any type of pathology, and even for unanimated samples based on the OPU recovery.Likewise, it was proved that the dual-wavelength OPU is capable of reconstructing objects with no need of unwrapping algorithms, up to the synthetic wavelength (which depends on the individual wavelengths).In this way, unwanted wrapped phase values are avoided, which in the classical DHM with a single wavelength are generated when the heights of the objects are greater than the wavelength itself.

Figure 1 .
Figure 1.Experimental arrangement for simultaneous recording of dual-wavelength holograms.

Figure 2 .
Figure 2. (a) Recorded digital hologram for a test sample; (b) detail of the intersecting fringes for both wavelengths; (c) Fourier space spectra corresponding to the simultaneous hologram with λ 1 = 532 nm and λ 2 = 638 nm.

Figure 3 .
Figure 3. Flow chart to record and reconstruct dual-wavelength holograms simultaneously.

Figure 4 .
Figure 4. SiO 2 thin step.Wrapped phase at (a) 532 nm, and (b) 638 nm, (c) unwrapped phase at 3.2 µm (synthetic wavelength), and (d) thickness line profile of unwrapped phase resulting from the dual-wavelength OPU method and filtering.

Figure 6 .
Figure 6.SC from a sample with KA signs: unwrapped phase obtained employing the dual-wavelength OPU.Details of the transverse phase profile in some areas are shown on the right.

Figure 7 .
Figure 7. Keratinocytes from SB and SS in a sample with KA signs.(a) Sample illuminated with a LED; (b) phase image from (a) retrieved at 638 nm with details of the phase profile for randomly selected cells; (c) sample illuminated with a LED; and (d) phase image from (c) retrieved at 532 nm, with detail of the phase profile of some cells, and 3D mesh (e) for cell number 5 in image (b), and (f) cell number 1 in image (d).

Figure 8 .
Figure 8. Characteristic lobules or keratin pearls in a sample with KA (a) illuminated with a LED, where keratinocytes are detected; wrapped phase at (b) 532 nm and (c) 638 nm; (d) characteristic lobules as unwrapped phase was obtained employing the dual-wavelength OPU, showing details on their phase profiles; (e) unwrapped optical phase of magnified lobule 2.

Figure 9 .
Figure 9. Keratinocytes in a sample with no KA signs: (a) illuminated with LED; (b) unwrapped phase image recovered at 532 nm, and (c) at 638 nm.

Figure 10 .
Figure 10.(a) Maximum and (b) average height variation; and (c) length of characteristic lobules in skin samples diagnosed with KA.Measurements obtained with the dual-wavelength OPU.

Table 1 .
Regions identified with and without KA signs.

Table 2 .
Measurements with DHM with dual-wavelength OPU in samples with and without KA signs.