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Abstract
This work develops a single-shot holographic profilometer that enables shape characterization of discontinuous deep surfaces. This is achieved by combining hologram frequency multiplexing and an illumination technique of complex amplitude in multi-incidence angle profilometer. Object illumination is carried out from seven directions simultaneously, where the radial angular coordinates of illumination plane waves obey the geometric series. It is shown that: (i) the illumination pattern provides the required frequency separation of all object wavefronts in transverse frequency space, which is necessary for hologram demultiplexing, and (ii) numerical generation of longitudinal scanning function (LSF) is possible, which has large measurement range, high axial resolution, and small side lobes. Low side lobes of LSF and the developed multiplexed field dependent aberration compensation method are essential to minimize the negative influence of speckle noise of single-shot capture on the measurement result. The utility of the proposed method is demonstrated with experimental measurement of heights of two step-like objects.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Digital holographic microscopy (DHM) is a suitable measurement technique for non-contact, short measurement time, and high accurate surface characterization of optical components. It has been shown that DHM give access to: (1) complete complex optical field information, (2) numerical refocusing, and (3) aberration correction of the measurement system [1–5]. These advantages have contributed to the wide applicability of DHM for shape measurements [6,7]. In DHM, the interference fringe pattern, which is registered by CCD/CMOS camera, encodes the information of the object shape. Surface reconstruction is obtained when the object phase image is numerically reconstructed in the designated plane and unwrapped [8,9]. However, conventional DHM systems have a limitation on measuring profiles discontinuities. For discontinuities higher than λ/4 in reflection mode of the system (λ - wavelength), the reconstructed object phase cannot be evaluated directly employing one-single illumination direction or one wavelength because of 2π ambiguity problem [10].
In order to solve the 2π ambiguity problem in DHM, multiple capturing of holograms with varying object illumination angle must be done, which sacrifice the feature of short measurement time. For example, optical contouring approach enables the measurement of large depth objects by using two holograms that have been recorded before and after a tilt of the object beam Δθ (Δθ<<1°) [11,12]. Each hologram is analyzed to obtain their individual phase, and thus, the obtained phases are subtracted. The resulting phase map has a larger unambiguous measurement range (UMR) [12]. However, phase noise is amplified, which might affect the axial resolution. Noise amplification is avoided when employing more than two holograms with different illumination angles as proposed by the multi-angle interferometry (MAI) [13]. MAI offers surface reconstruction with improved axial resolution and increased UMR than optical contouring. Nevertheless, the range of usable angles is very small (∼0.50 − 1°), which still limits the axial resolution. Recently, the multi-incident digital holographic profilometry (MIDHP) has been proposed for solving the limitation of axial resolution of surface topography reconstruction in DHM [14]. The topography of the object is recovered by finding the maxima of longitudinal scanning function (LSF) along the optical axis [14–20]. However, experimental realization of MAI and MIDHP showed that a minimum of six holograms are required for obtaining large UMR and resolution of a few micrometers.
In this work, we develop a single shot holographic profilometer (SSHP) with axial resolution below one micrometer and large UMR. This is achieved by simultaneously illuminating the object from seven different directions. Such an illumination requires independent modulation of amplitude and phase that can be realized from a phase only spatial light modulator (SLM) using complex-amplitude modulation technique [21,22]. The technique utilizes arithmetic manipulation of phase signal encoded on the SLM and physical frequency filtering, which is experimentally realized in the proposed setup. The employment of the phase SLM with complex-amplitude modulation allows building a compact system for hologram multiplexing. Hologram multiplexing can be carried out in time [23,24], space [25,26] or spatial-frequency domain [27,28]. Here, we follow the concept of frequency multiplexing, where the frequency domain is divided to store a set of optical signals. Hologram frequency multiplexing has been successfully applied for hologram compression [29,30], optimizing spatial bandwidth capacity [31], increasing Field of View [32,33], improve measurement time in digital holographic tomography [34], color imaging [35], or multiplexing different imaging modalities [36]. Single exposure hologram multiplexing might be physically realized by dividing beams with beam splitters [32,33], or diffractive gratings [34,36]. Using set of beam splitters even four object beams can be multiplexed into single hologram [33], but the system becomes complicated. In this work, we show that it is experimentally possible to multiplex seven object beams in a single optical wavefront using phase only SLM.
Proposed multiplexing approach enables building the SSHP system that registers required information to complete shape characterization with large UMR and sub-micrometer resolution from a single frame of multiplexed digital hologram (MDH). In the system, an object is illuminated by set of specially selected seven plane waves. With this set of plane waves, high performance multiplexing and good metrological parameters of LSF can be obtained. In the frequency domain, the angular components of these plane waves are distributed on a spiral and their longitudinal frequencies obey the geometric series, where the first component is close to the optical axis and the last is the most off-axis. This approach results in series of large transverse frequencies, and thus it provides good frequency separation of all object wavefronts in transverse frequency space. The illumination pattern allows controlling the side lobes of the LSF at the level of the half of the maximum value. Such low side lobes are essential to minimize the negative influence of speckle noise on the measurement result. The use of high illumination angles, above 30°, requires the correction of field dependent aberrations [37]. For this multiplexed field dependent aberration compensation method was developed, where hologram of a mirror object is captured, demultiplexed and used for compensation. This work is structured as follows: Section 2 provides information about developed single shot DH profilometer; Sections 3 and 4 present the fundamentals of the illumination pattern engineering and selection of angles for 7-beams illumination; Section 5 shows multiplexed hologram generation; Section 6 explains demultiplexing process of the captured hologram; Section 7 outlines numerical analysis of LSF; Section 8 presents experimental results, and Section 9 provides the conclusions.
2. Single-shot digital holographic profilometer
Figure 1 presents the single shot DH profilometry system, in which the multi-interference pattern is captured by the image sensor as a single MDH. The configuration of the measurement system is based on Twyman-Green interferometer. Before the collimated beams reach the main part of the measurement system, the light beam is generated by a laser light source (λ = 532 nm) and is filtered by a spatial filter and transformed into plane wave by a collimating lens. Then the collimated beam (green arrow) is split into reference (blue arrow) and object (red arrow) beam.
Fig. 1. Scheme of the SSHP system. ILS – illuminating system, IMS – imaging system, SLM – phase-only spatial light modulator, L – lens, f – focal length, F – amplitude filter, MREF – reference mirror, W – optical wedge, MO – microscope objective, CMOS – detector.
The main part of the system, which is presented below, consists of two important elements: (i) illumination system (ILS), and (ii) imaging system (IMS). The illumination system consists of (i) phase only SLM (Holoeye, 4160 × 2464 pixels, 3.74 µm, SLM), (ii) 4f system (two lenses L with the same parameters: fL = 122 mm, ∅︀ = 25 mm), and (iii) amplitude filter (F), which is placed in the Fourier plane of the 4f system for removal of -1 and 0 diffraction orders. The SSHP system utilizes ILS to produce object illumination that is a sum of seven plane waves of desired frequencies in X and Y directions. In Fig. 1, the left collimated beam, that is treated as an object beam, is directed to the SLM by an optical wedge (W1), then the beam is reflected from the surface of the SLM. SLM is slightly tilted with the aim to align the first diffraction order onto the optical axis. Seven illumination beams are generated because of the complex-amplitude modulation technique, which encodes complex amplitude distribution of seven-illumination object beams using the SLM. The main orders of diffraction beam are ±1 and 0 orders. Orders zero and minus one are filtered out when using the filter F, as shown in the enlarged part of Fig. 1. The unblocked diffraction order one is optically Fourier transformed by the second lens L, and hence, at the image plane of the ILS we obtain the seven beams illumination pattern.
The second part of the system is the IMS, which consists of: (i) optical wedge W2, (ii) afocal system built from a microscopic objective (working distance 5.2 mm, fMO = 4 mm, NA = 0.75, 50×, MO) and LA lens (∅︀ = 50 mm, fLA = 200 mm) that has transverse magnification M = 49.9, (iii) CMOS camera. Input plane of the IMS, which is located at the front focal plane of lens LA, is placed at the image plane of the ILS. The measured object is placed in the focal length of MO, and thus, object and detector plane are conjugated. After leaving the 4f system of ILS, illumination wavefront travels along the optical axis through the IMS until it reaches the surface of the object. The geometry of the sample used in this work is shown at the down right corner of Fig. 1. The sample is a step-like five levels reflective object. The reflecting multiplexed object beam comes back through the afocal system and is steered towards the CMOS camera (JAI GO-5101M PGE, 2464 × 2056 pixels, 3.45 × 3.45 µm2, sensor Sony IMX264) by the wedge W2. Moreover, the reference beam is tilted in such a way that the object beam is outside of the zero and correlation orders (>3NA, NA – numerical aperture of the optical system), and thus, the entire object beam can be retrieved from the MDH. Multiplexed object and reference beams interfere, and the fringe pattern is registered by CMOS camera at the back focal length of the LA. Frame rate of the camera is given by 20 fps resulting in single hologram acquisition time of 50 msec.
3. Illumination pattern engineering
The 7-beams object illumination pattern contains seven plane wave components
It is assumed that all higher diffraction orders (q > 1) are neglected due to the lower diffraction efficiency. The above equation indicates nonlinear distortion of the amplitude determined by the corresponding Bessel function. The distortion dims the value of the desired amplitude. Since our illumination pattern is composed of plane wave components of equal amplitudes, the distortion can be corrected to have the desired value of amplitude A. The object wave illumination along the optical axis at the object plane (x, y) is obtained when considering the tilt of the SLM and magnification of IMS. Thus, the object illumination pattern is given as
where4. Selection of angles for a 7-beam illumination pattern
Reference [14] investigated sequential capturing strategy based on the geometrical series, where the illumination angles in transverse frequency space were aligned along one line and all were positive. Thus, the used transverse spatial frequencies were very close to each other. In this work, we make effort to optimize frequency separation of the illumination wave components into the NA of the IMS for generating a LSF with large UMR and high axial resolution.
Here, illumination pattern is also designed with the geometrical series, however all illumination angles are packed into one complex wave illumination. This enables single-shot solution, high longitudinal resolution, reduced side lobes, and large UMR at the same time. The geometric series results in longitudinal frequency components of wave vectors kp as
where Δkz = kzmax - kzmin, kzmin = 9.76 µm-1 and kzmax = 11.79 µm-1 are limiting values of the series, and r is the progression parameter. Reference [14] proposed the geometrical series where the first element is kzmin, while the series generated with the Eq. (7) starts with kzmax. This modification improves the single-shot solution, i.e., it provides better frequency separation of all illumination components in transverse frequency space. The geometric series defines values of longitudinal frequency components. The separation of kp in transverse frequency space can be achieved when the illumination components for p ɛ {1, …, 7} have azimuthal angles ${\gamma ^{(p)}} = 1/4\pi + 1/3(p - 1)\pi$. The radial angular frequencies are given as $k_{ri}^p = {({k_0^2 - {{(k_{zi}^p)}^2}} )^{1/2}}$. Corresponding transverse frequencies are then $[{k_{xi}^p = k_{ri}^p\cos {\gamma^{(p)}},\textrm{ }k_{yi}^p = k_{ri}^p\sin {\gamma^{(p)}}} ]$. Amplitude and phase distribution of numerically generated 7-beams illumination pattern is illustrated in Figs. 2(a) and 2(b). The distribution of frequencies in the Fourier domain is presented in Fig. 2(c).Fig. 2. 7-beams illumination pattern: a) amplitude, b) phase, and c) frequency distribution, the circle shows the NA limit of IMS.
Figure 3 shows the corresponding LSF calculated as
where z is the axial distance between object surface and in-focus position of the measurement system.Fig. 3. (a) Maximum values of side lobes as a function of progression parameter r in the depth range z ∈ (1, 24), (b) the distribution of LSF for r = 1.78.
To determine optimal value of the progression parameter r, the height of side lobes was investigated numerically. Figure 3(a) illustrates the maximum values of the side lobes as a function of r in the depth range z ∈ (1, 24). The optimal value r = 1.78 was determined as a central part of the global minimum. The plot in Fig. 3(b) illustrates practical properties of LSF: (i) axial resolution zres = π/2Δkz = 0.77 μm [20,39], (ii) side lobes, which are below 0.53, and (iii) large measurement range, which equals to 24.6 μm. Small side lobes are especially important to minimize negative influence of speckle noise on the experimental LSF.
5. Multiplexed digital hologram generation
In the developed SSHP system, the 7-beams illumination pattern, given by Eq. (4), is reflected from the surface of the measured sample producing seven object beams as
The reference wave is a plane wave having frequency component fRx in x direction only, which is sufficiently large to shift entire object wave field outside of zero and correlation orders (fRx >3NA/λ). MDH is a discrete real-valued signal that is recorded in a single frame on CMOS. The experimental intensity pattern for the measured object is presented in Fig. 4(a) as full image and selected zoom area. MDH encodes all object waves as the complex-valued signal in the object term OR*. Its Fourier spectrum with removed carrier reference wave is shown in Fig. 4(b). The used colormap in MATLAB is ‘cubehelix’, which is friendly for colorblind readership [40].
Fig. 4. a) Intensity distribution of MDH, b) Fourier spectrum of object term of MDH, c) filter Wp for retrieving individual object beams from the MDH.
6. Demultiplexing and aberration correction of MDH
This section discusses numerically aided experimental demultiplexing technique of MDH that is registered for measurement of step-like samples. The technique provides reconstruction of seven object beams, where each corresponds to its illumination angle. Demultiplexing process, starts with the Fourier Transform (FT) of MDH that is multiplied with reference wave. In Fourier domain, presented in Fig. 4(b), the spectrum of the object field shows the seven components of the object term. The position of each spectrum component depends on the illumination angle. According to the position of the desired spectrum, a demultiplexing filter WP was designed, which is applied to recover individual object beams. Its frequency distribution is illustrated in Fig. 4(c), where different colors illustrate regions of validity of the filters. Parameters of reference wave and filter distribution are found in the calibration process. The demultiplexing filter WP is applied to recover individual object beams as
where IFT is an inverse FT, R(x, y) is the reference plane wave with frequency components [fRx, fRy].In Eq. (12), the subscript ‘abr’ stands for coded aberrations in the object hologram. The use of large illumination angles, above 30 deg, requires compensation of aberrations, which are field dependent. Wave aberrations corresponding to each illumination angle are measured in the calibration process. These measured aberrations are subtracted from the reconstructed object beams as
where $\theta _{abr}^p$ is the corresponding phase aberration. As a result, seven compensated object wavefronts are reconstructed. The steps of the demultiplexing process are presented in Fig. 5. The upper row shows frequency distributions of measured aberrated object beams. The middle row illustrates spatial distributions of the aberrated object beams and field dependent aberrations. Finally, the last row shows the reconstructed and aberration compensated set of seven object beams.Fig. 5. Demultiplexing process: a) filtration in Fourier domain of single beams, b) object and compensating reconstructed phases, c) final reconstructed phase after aberration compensation.
The calibration procedure (presented in Fig. 6) is divided into two steps. Step one is based on single and on-axis illumination beam acquisition, while the step two uses 7-beams illumination pattern. During the calibration procedure, two holograms for flat reflective object and for both types of illumination are acquired. In our case, mirror object (surface flatness λ/10), which is placed in in-focus position of MO, is used. In the step one, two parameters are determined: (i) frequency components of the reference wave [fRx, fRy], and (ii) outer limit of the demultiplexing filter WP. While during 7-beams acquisition step, (i) frequencies $[k_{xi}^p,k_{yi}^p]$ of the illumination beams, (ii) wavefront aberration, and (iii) demultiplexing WP filter, are evaluated.
Fig. 6. The scheme of the calibration procedure: a) step 1 – on-axis hologram acquisition; b) step 2 – multi-beam acquisition.
The acquired hologram for on-axis illumination enables finding accurate parameters of the reference wave [fRx, fRy]. The applied calculations are divided into two parts: finding location of maximum in Fourier domain of the hologram and plane wave fitting of the recovered phase of the reference wave. Second element improves accuracy of calculations. The obtained reference wave is applied in the 7-beams calibration step, which has two sub-steps. In these two sub-steps frequency components $[k_{xi}^p,k_{yi}^p]$ of 7-beams illumination pattern and the set of field dependent aberrations are found. In the first sub-step the theoretical distribution of the filter Wp is used. For finding its frequency distribution the initial values of frequencies $[k_{xi}^p,k_{yi}^p]$of 7-beams illumination pattern are employed. The filter areas of Wp are determined using the criterion of the smallest distance to the corresponding frequency of illumination. The experimental measures of $[k_{xi}^p,k_{yi}^p]$ are then determined by finding locations of maximum in Fourier domain of the hologram within area of corresponding filter Wp and plane wave fitting of the recovered phases of the illumination waves. The experimentally obtained set of angles of illumination pattern presented as polar angles is [3.2°, 22.47°, 28.14°, 31.19°, 32.59°, 33.03°, 34.13°], respectively. The corresponding theoretical values are [3.22°, 22.59°, 28.24°, 30.99°, 32.45°, 33.23°, 34.22°]. It can be noted that the discrepancy is very small. Found parameters of illumination pattern are used for determining final shape of the filter Wp. In the second sub-step the same hologram is used. The field depended aberrations are retrieved during the demultiplexing process based on Eq. (11), where phases of the aberrations are reconstructed for each illumination wave. The calibration part is not an integral part of measurement process of inspected sample, which means that it does not have to be done before each measurement.
7. Shape reconstruction based on LSF
Demultiplexing of the object fields is required for the shape reconstruction algorithm, which is based on generation, refocusing and analysis of the LSF. The refocusing part is carried out by numerical propagation of individual object fields$u_{BL}^p(x,y,0)$. This is accomplished with Rayleigh–Sommerfeld integration method [3]
In summary, the algorithmic part of the shape reconstruction algorithm consists of the following steps: (i) recovery of the complex object waves $u_{BL}^p(x,y,0)$ with hologram demultiplexing procedure, (ii) setting the phases to zero at the focus point (iii) propagating the wave fields to the parallel planes using Eq. (14) within UMR, (iv) calculating the LSF at each distance using Eq. (15), and (v) finding and storing the maximum values LSF(x, y, z) ∼ 1 for each spatial coordinate as the height measurement. To minimize noise effect, we apply linear moving average filter of axial depth Δz ≈ zres/4. The propagation step is 0.05 μm. Disadvantage of the proposed multiplexing solution is reduction of the transverse resolution. The demultiplexed object fields, which are used for the shape reconstruction, have decreased frequency bandwidths. Their bandwidths can be analyzed using point spread function (PSF), that is a response to an intensity point object. The Full Width at Half Maximum (FWHM) of PSF of the imaging system without filters equals 0.48 um. For comparison, the average FWHM evaluated for multiplexing solution and for all filter components are 1.26 μm and 1.29 μm for X and Y directions, respectively. This reduction of bandwidth limits the resolution of the reconstructed shape. We have analyzed this effect with the simulations of shape reconstruction of a circular step object, which has different diameters and height of 1 μm. Using the demultiplexing solution it was possible to reconstruct shape of diameter 1.3 μm and larger. Whereas without multiplexing solution, that is with seven object beams captured separately, reconstruction of object of minimum diameter 0.6 μm was possible.
8. Experimental results
This section presents applicability of developed technique. The objects used for experimental verification of our measurement concept are two microelements of five steps each. The geometry of these objects is shown in Fig. 1 (see Section 2). The step-like objects have been fabricated using 3D two-photon photolithography technique, in which two-photon absorption leads to solidification of a liquid polymer near to the focus of a femtosecond-pulsed laser beam [41]. Both samples are fabricated on the same plate, which has been sputter coated with ∼50 nm layer of gold to obtain reflectivity of the sample. The selected step-like objects have been manufactured with 0.5 μm and 4 μm height difference between subsequent steps, respectively. Extracted amplitudes (Figs. 7(a) and 7(c)) and phase distributions (Figs. 7(b) and 7(d)) from acquired MDH for both objects are shown in Fig. 7. In our experiment, different distributions of 7-beams illumination were used for each object, which is visible in the reconstructed phases.
Fig. 7. Complex field of multiplexed object holograms: a) amplitude and b) phase for object of step Δh = 0.5 µm; c) amplitude and (d) phase for object of step Δh = 4 µm.
To reconstruct the surface of the first object, for which height difference between subsequent steps equals 0.5 μm, multiplexed holograms of object and reference surface were captured by employing the polar angles of the wave vector discussed in Section 4. For the multiplexed object hologram, surface five (the highest surface) was placed at the in-focus position of MO. The hologram is acquired by CMOS camera, which is placed at the back focal length of the lens LA. During height reconstruction, the propagation step is set to z0 = 0.1 μm for scanning the z-axis range [-4, 1] µm. 2D surface reconstruction is shown in Fig. 8(a). Horizontal and vertical cross sections through reconstructed object are presented in Figs. 8(b) and 8(c). The absolute reconstructed heights of the object from surface one to five are 0 μm, 0.39 μm, 0.89 μm, 1.36 μm, and 1.75 μm. The proposed aberration compensation method enables proper reconstruction of the phase object fields, which is visible in Fig. 5(b). Removal of aberrations allows for a more accurate height reconstruction result.
Fig. 8. a) 2-D reconstruction of the step-like object with Δh = 0.5 µm, b) horizontal cross sections of reconstructed object (A-A, B-B), and c) vertical cross sections of reconstructed object (C-C, D-D, E-E).
The second measured object (Δh = 4 µm) is significantly higher than the earlier object. Since this new object is too deep, the aberration wavefront depends on depth as well. When surface five of the object is focused, the shape of the corresponding aberration will be strongly deformed by propagation effects. To minimize the deformation of aberration wavefront, the in-focus plane was set on surface three of the object. For surface reconstruction of second object, previous illumination angles were employed. However, during demultiplexing process it was observed that the largest illumination directions generate large shadows areas over lower structures of the object. When extracting the field information, these shadowed areas retrieve only phase noise, which prevents from reconstructing correctly the object surface. To minimize the shadowing effect, the polar angles of the wave vector were changed according to the values kzmax = 11.7918 µm-1 and kzmin = 10.159 µm-1. The changes in the limiting values of kz allows recalculating the polar angles as [3.22°, 20.45°, 25.46°, 27.89°, 29.15°, 29.83°, 30.66°] and corresponding resolution is estimated as zres = π/2Δkz = 0.96 μm. This illumination pattern reduces the extent of shadows on the object. Due to the change in illumination angles, it was necessary to re-register the multiplexed hologram for the dependent aberration compensation method. Reconstruction of the object was carried out with new set of angles, and propagation step z0 = 0.1 μm for scanning the z-axis range [-10, 10] µm. With these adjustments, the surface of the object was successfully reconstructed as shown in Fig. 9(a). Horizontal cross sections through the height reconstruction are presented in Fig. 9(b) while Fig. 9(c) depicts the vertical cross sections. The reconstructed heights of the measured object are 0 μm, 4.06 μm, 8.22 μm, 11.97 μm and 16.1 μm (heights in reference to the surface one).
Fig. 9. a) 2-D reconstruction of the step-like object with Δh = 4 µm, b) horizontal cross section (A-A, B-B), and c) vertical cross sections (C-C, D-D, E-E).
Previously, Ref. [42] has shown that is possible to employ five illumination beams for recovering the first step like object. However, the five-beam illumination pattern generates side lobes in the LSF larger than the half of the maximum value of the LSF, which results in stronger influence of speckle noise on the measurement result. On the other hand, employment of more than seven multiplexed beams will reduce the available bandwidth for each multiplexed beam, which will impact the resolution of the extracted phase, and thus, the quality of reconstructed object might not be optimal.
9. Conclusions
This paper presents the SSHP method that uses a single hologram. The method is based on the concept of the multi-angle interferometry, where a set of holograms with different illumination angles are used for shape retrieval of discontinues surfaces. Notably, SSHP enables measurements of micro-objects with large depth and sub-micron resolution using a single frame.
The single shot measurement feature is obtained through development of multiplexed holographic system and demultiplexing processing. The multiplexing holographic system is based on a built-in module of complex amplitude illumination that provides simultaneous object illumination from seven distinct directions. The 7-beams object illumination pattern is distributed on spiral-like shape in NA of the optical system. Successive illumination plane waves are characterized by a difference in azimuthal angles equal to 60°, whereas distribution of polar angles obeys the geometric series of their corresponding longitudinal frequencies. It has been shown that when employing spiral-like illumination, high performance multiplexing is achieved. Thus, it is experimentally proved that multiplexing of seven object beams in a single captured hologram is possible. However, the disadvantage of this multiplexing solution is reduction of the transverse resolution, which limits the resolution of the reconstructed shape. It is worth noting that combination SLM-MO allows setting corresponding constraints to have a LSF with good metrological features, i.e. sub-micrometer resolution and low side lobes. To decrease the cost of the experimental implementation a HD SLM might be used instead of 4K SLM. In Ref. [14], Holoeye Pluto of HD resolution was used for tilting illumination beam up to 40°.
Demultiplexing process is carried out by employing a set of band pass frequency filters, which are calculated within developed calibration, which is performed before the measurement. To measure depth objects with high resolution, illumination pattern must have large off-axis angles. For this multiplexed field dependent aberration characterization and compensation methods were developed, which are integral parts of the calibration and demultiplexing processing. Finally, shape reconstruction is based on the numerical generation and analysis of LSF. However, the SSHP is more sensitive to the speckle noise. To counter this deficiency, LSF with small height of side lobes had to be selected. With the proposed illumination scheme, LSF with high axial resolution, large UMR and small side lobes is obtained. As a result of this methodology, discontinuous surfaces can be characterized with sub-micron resolution. The sample under investigation must have depths contained within UMR, here 24.6 μm.
Funding
HoloTomo4D (2015/17/B/ST8/02220); MSIT Program of Korea (IITP, No. 2020-0-00981); Warsaw University of Technology.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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