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Abstract
This study provides a detailed comparison of two widely used quantitative phase imaging (QPI) techniques: single-shot off-axis digital holographic microscopy (DHM) and digital lensless holographic microscopy (DLHM). The primary aim is to evaluate and contrast critical aspects of their imaging performance, including spatial phase sensitivity, phase measurement accuracy, and spatial lateral resolution. Employing typical configurations for both DHM and DLHM, the study utilizes a customized phase test target featuring linear phase changes introduced by a specially designed linear density attenuation filter. Ground truth data from an atomic force microscope is incorporated to validate the experimental findings. The comparative analysis reveals that DHM and DLHM exhibit nearly identical spatial phase sensitivity, with DHM demonstrating a minimal 3.2% measurement error compared to DLHM's 4% in height measurement accuracy. Notably, DHM achieves a finer spatial lateral resolution down to 3.1 µm, surpassing DLHM's 5.52 µm. While DHM outperforms DLHM in precision and resolution, the latter offers advantages in terms of portability and cost-effectiveness. These findings provide valuable insights for researchers and practitioners, aiding in the informed selection of QPI methods based on specific application requirements.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Quantitative phase imaging (QPI) techniques offer a means to generate high-contrast images of transparent objects by leveraging the phase change of an optical wavefield resulting from path differences in light transmission or reflection through/from the samples [1]. These images provide valuable insights into the sample's refractive index and thickness variations [2]. QPI enables non-invasive imaging of specimens without fluorescent markers or dyes [3]. In this way, QPI techniques allow label-free imaging, preserving the natural state of cells and facilitating real-time observations of dynamic cellular processes [4–6]. This label-free and non-invasive nature of QPI is particularly advantageous in biological studies, as it minimizes potential cytotoxicity and disturbances caused by exogenous contrast agents. Furthermore, QPI allows for quantitative analysis of cellular properties such as cell morphology, refractive index distribution, and intracellular organelle dynamics [7], providing helpful information for various biological and biomedical applications.
The conventional approach to acquiring QPI measurements involves the use of off-axis Digital Holographic Microscopy (DHM). These systems offer the advantage of rapid and accurate quantitative phase imaging in a single shot. Operating on the principles of optical interferometry, DHM systems reconstruct both amplitude and phase distributions of various specimens, including biological and non-biological samples [8]. DHM stands out in the realm of QPI techniques due to its high sensitivity, large imaged field of view, and the ability to achieve high frame rate acquisition [9]. Its robustness and nanometric sensitivity in phase measurements have facilitated dynamic imaging applications, such as three-dimensional (3D) particle tracking [10], cell motility studies [11], and dynamic changes in surface topography [12]. Over the past decade, DHM has evolved into a mature technology, benefiting from extensive research focused on its optical design, phase reconstruction algorithms, and diverse applications in life and materials sciences [13,14]. Despite its successful performance, the broader applicability of DHM in in-situ clinical research has been hindered, in part, by the necessity for robust setups, specialized equipment, and the associated volume and size requirements. The specialized nature of the elements required by the technique and its need for dedicated and sometimes bulky instrumentation presents challenges for integration into clinical environments where space constraints and ease of use are essential considerations.
To overcome the constraints of traditional DHM, recent advancements in computing power have facilitated the development of portable and cost-effective QPI implementations. Lensless microscopy techniques, operating under digital holography principles, have emerged as a viable solution. These methods utilize a point source of spherical waves to illuminate the sample, which is then recorded by a digital camera to capture the resulting diffraction pattern [15]. Lensless microscopy architectures vary based on the sample's location along the axis defined by the point source and the digital sensor. On-chip microscopy places the sample close to the sensor, providing a large field of view limited only by the recording media's physical size [16]. However, resolution is constrained by the sensor's pixel size, often necessitating super-resolution techniques [17] or multi-shot recording procedures [18]. Alternatively, in Digital Lensless Holographic Microscopy (DLHM) [19], where the sample is positioned near the point source, the magnification of the diffraction pattern avoids the need for resolution-enhancing methods. Unlike on-chip microscopy, DLHM's lateral resolution is determined by the system's geometrical configuration [19]. While lensless techniques offer hardware simplicity and cost-effectiveness [20,21] for visualizing micrometer-sized samples, they introduce computational complexity during reconstruction, especially for DLHM [22]. Digital retrieval of sample information involves an inverse diffraction process, demanding diffractive numerical propagation methods to account for the high-NA sphericity of the illumination wavefront in DLHM.
In recent literature, numerous studies have undertaken comparative analyses of various Quantitative Phase Imaging (QPI) methods, concentrating on specific applications. For instance, in [23], the authors conducted a comprehensive investigation of three distinct phase imaging methods, including one based on the transport-of-intensity equation (TIE) [24], quadriwave lateral shearing interferometry (LSI) [25], and DHM. The study successfully characterized the refractive index profile of optical waveguides, demonstrating the accuracy and precision of these techniques for refractometry. In [26], a microscopic setup combining DHM and TIE for quantitative phase imaging was reported. The comparison of DHM and TIE on live cells highlighted the strengths and limitations of each method, providing insights into visualizing specific specimens correctly. Furthermore, the advantages of quantitative phase imaging in monitoring adherent mammalian cell cultures were explored in [27], comparing DHM, lens-free microscopy [28], and quadriwave LSI. These works have significantly contributed to understanding the capabilities and limitations of various QPI techniques in specific contexts. However, despite these and other comparative studies, it is noteworthy that, to the authors’ best knowledge, there is a gap in the direct comparison of the performance of DLHM and DHM. While existing research has extensively explored the strengths and weaknesses of different QPI techniques, the specific evaluation of DLHM against DHM remains unaddressed, particularly regarding imaging performance.
This investigation aims to fill this void by concentrating on evaluating the performance of the above-mentioned QPI methods. This work seeks to provide a focused and direct comparison of DLHM and DHM concerning pure imaging performance metrics, shedding light on their performance distinctions. The comparative analysis includes an in-depth examination of DHM and DLHM, specifically emphasizing spatial phase sensitivity, phase measurement accuracy, and spatial lateral resolution. The study utilizes ground truth data from an Atomic Force Microscope to validate the findings, shedding light on the inherent trade-offs between imaging performance and hardware-software complexity of each technique. The paper is organized as follows: Section 2 provides an overview of the selected QPI methods, details the process of recovering topography information, and outlines the methodology for quantifying their imaging performance. Section 3 presents the experimental results of the selected variables for evaluating imaging performance. The paper concludes with a summary of the findings in the concluding section.
2. Quantitative phase imaging methods
This study focuses on two QPI methods: interferometry-based off-axis Digital Holographic Microscopy (DHM) and diffraction-based Digital Lensless Holographic Microscopy (DLHM). These single-shot techniques are further evaluated using measurements obtained from an Atomic Force Microscope (AFM), serving as a reliable ground truth reference for assessing thickness changes. Figure 1 presents illustrative schemes of the optical setups implemented for DHM and DLHM.
Fig. 1. Schemes of the optical setups: a) DHM and b) DLHM. BE Beam expander, BSX Beam splitters, MX mirrors, MO Microscope Objective and TL tube lens.
2.1 Off-axis digital holographic microscopy
DHM is an imaging technique used to extract the complex amplitude wavefield of light scattered by microscopic objects. A Mach-Zehnder interferometer is commonly employed for imaging biological samples [8], such as transmission or phase samples, as shown in Fig. 1 a). In this setup, a collimated beam emerging from a laser is divided into two light paths by the first beam splitter (BS1). The first path is the reference arm of the interferometer, in which a plane wave travels undisturbed until the first mirror (M1). M1 reflects the light towards the second beam splitter (BS2), which introduces a tilting angle between the object wavefront along the x- and y-axes. The second path is the object arm. In this path, the light travels until the second mirror (M2) and through the sample. Then, an infinity-corrected Microscope Objective (MO) lens and a Tube lens (TL) are used to collect the light scattered by the sample. The MO and the TL lenses are set up in the telecentric configuration, forming a 4f-like system, so the TL corrects the spherical wavefront distortion introduced by the MO lens [14]. Then, the object wavefront travels until the BS2, where it merges with the plane reference wave. The optical interference between the object and reference waves is recorded on a CCD/CMOS sensor located at the back-focal plane of the TL.
In DHM, the hologram distribution h(x,y) recorded onto the digital sensor is:
In Eq. (2), $k = 2\pi /\lambda $ is the wave number being λ the source's wavelength, $({m,n} )$ are the discrete lateral coordinates of the sensor, and $({\Delta x,\Delta y} )$ are the pixel pitch in each dimension. The tilting angle (${\theta _x},\textrm{}{\theta _y}$) in off-axis holograms can be estimated by the hologram size and the center position (i.e., maximum position) of the +1-diffraction term [29],
Given that image-plane holograms are recorded, the computational reconstruction of these holograms does not necessarily demand numerical propagation to focus the object information. This phenomenon is due to the spatial filtering of the DHM hologram, which enables the retrieval of the complex wavefield scattered by the sample. This process is grounded in the interferometric nature of the technique, where the fringe pattern serves as the carrier of information. Utilizing inverse methods enables the demodulation of this encoded information, providing the necessary data for refocusing the sample computationally. For a more in-depth exploration of the 3D recovery capabilities of DHM, interested readers are directed to [30] and [31].
Returning to Eq. (3), a critical process in the compensation task in off-axis telecentric-based DHM is finding the accurate spatial frequency components $({{f_x},{f_y}} )$ to avoid phase reconstructions with distortions [32]. Several algorithms have been proposed for this accurate spatial frequency determination, primarily based on heuristic searches [29,33,34], learning-based methods [35,36], brute-force approaches [37,38], phase variation minimization [39], geometrical transformations [40], among many others. For further details on the hardware aspects of DHM, consult [14]. For a comprehensive understanding of the numerical reconstruction procedures, refer to [30]. Once the complete complex wavefield of the studied sample is recovered, its amplitude $A({x,y} )= |{o({x,\; y} )} |$ and phase $\varphi ({x,y} )= {\tan ^{ - 1}}\left( {\frac{{Im\{{o({x,\; y} )} \}}}{{Re\{{o({x,\; y} )} \}}}} \right)$ measurements can be accessed.
2.2 Digital lensless holographic microscopy
DLHM provides a simple imaging setup for extracting information from microscopic specimens without needing lenses for magnification purposes [19]. In this setup, a monochromatic spherical wavefront with wavelength λ originates from a point source and illuminates a translucent sample positioned at a distance z, typically a few thousand wavelengths away from the source (see Fig. 1 b). In this technique, the digitally recorded information comprises the pure diffraction pattern of the sample resulting from the wavefront diffracted by the illumination source. This contrasts conventional DHM, where the recording involves an interferogram between two wavefronts. Various methods can be employed to generate the point source in DLHM, such as the use of micrometer pinholes [19], Blu-ray optical pickups [41], LEDs [16,42], GRIN lenses [43], SLED sources [44], fiber optics ends [45], holographic optical elements [21], standard laser diodes [46], or laser diodes in combination with tunable lenses [47], and many others. Once the illuminating spherical wavefront is generated, it interacts with the sample, scattering to form a magnified diffraction pattern on a digital sensor positioned at a distance of L from the point source [19]. This diffraction pattern, known as the DLHM hologram, encodes the complex amplitude wavefield of the studied sample. Mathematically, this complex amplitude wavefield o(x,y) can be expressed through the Rayleigh-Somerfield diffraction formula, Eq. (4).
In Eq. (4) $({x^{\prime},y^{\prime}} )$ are the lateral spatial coordinates at the sensor plane. The free-space magnification of the diffraction pattern in Eq. (4) is determined by the ratio $M = L/z$. This value of M has to be chosen such i) the diffraction pattern is correctly sampled by the digital camera and ii) the magnified region of interest of the sample fits in the digital camera. For DLHM to function effectively, careful consideration must be given to these two geometrical conditions and the constraint that imaging is limited to weak scattering samples [48]. The recording stage produces the intensity distribution recorded at the digital camera plane:
with ${\ast} $ denoting the complex conjugate. After the camera sensor records this diffraction pattern, subsequent numerical processing is necessary to recover the object information o(x,y) at the sample plane. Following the principles of holography, the information of the sample $o({x,y} )$ is reconstructed in DLHM by evaluating the diffraction process that a converging spherical wavefront $\frac{{{e^{ik({x^{\prime},y^{\prime}} )}}}}{{|{({x^{\prime},y^{\prime}} )} |}}$ undergoes as it illuminates the in-line hologram $h({x^{\prime},y^{\prime}} )$ and propagates toward the sample plane. In the case of low numerical aperture (NA) systems, the propagation of $h({x^{\prime},y^{\prime}} )\textrm{}$ to the sample plane can be achieved using the conventional angular spectrum formalism, allowing for the recovery of $o({x,y} )$. In scenarios characterized by larger NA and spherical wavefronts, which are particularly relevant in DLHM, specific propagation routines must be employed, as discussed in previous studies [49–51]. In these algorithms, the diffraction process described above can be numerically characterized by employing a discretized version of the scalar diffraction formula:Detailed information regarding the DLHM hardware and numerical processing can be found in [50,52–55].
2.3 Recovery of topography information and imaging performance
In both DHM and DLHM, once the phase information $\varphi $(x,y) is computed from $o({x,y} )$, it can be utilized to calculate the topography of each point within the observed field of view. This is achieved by employing the relationship between phase difference $\varphi $, the refractive index of the sample ${n_s}$, and its thickness t, as described by Eq. (7).
In Eq. (7) ${n_m}$ represents the refraction index of the medium surrounding the sample, which is typically assumed to be ${n_m} = 1$. This expression assumes the presence of homogeneous media and monochromatic illumination for recording the digital holograms.
In this study, to evaluate the performance of the selected QPI methods, lateral resolution [56] and phase sensitivity are used as figures of merit. Phase sensitivity is typically evaluated by measuring the background noise in the resulting phase images [1,7]. On the other hand, the theoretical determination of lateral resolution is governed by the diffraction limit, which can be expressed using Abbe's formulation, as shown in Eq. (8).
In Eq. (8), λ represents the illumination wavelength. The determination of NA differs between DHM and DLHM setups. In DHM, the numerical aperture is determined by the microscope objective (MO) [57,58], while in DLHM, it is influenced by geometrical factors, such as the source to sensor distance L, and the size of the digital sensor [19]. Equation (8) applies when the imaging systems are primarily governed by diffraction, and the Nyquist theorem does not limit the lateral resolution defined by Abbe's formulation. This study assumes that the spatial resolution is predominantly limited by diffraction, which is the case for DHM and DLHM, considering their conventional configurations and used sensors.
3. Experimental results
3.1 Experimental sample
A customized phase test target is employed as a study sample to measure and compare the measurement accuracy, spatial resolution, and spatial phase sensitivity of DHM and DLHM. This customizable phase calibration target was fabricated using a silver-halide photosensitive film and LED illumination. Derived from a commercially available amplitude-positive USAF test target, this target incorporated linear phase changes in different regions. A specially designed linear density attenuation filter, whose structure was numerically designed and projected onto an amplitude Spatial Light Modulator (SLM) was used in the photolithographic process to incorporate these changes, Fig. 2(a), the density filter's structure was then projected onto a photosensitive film using a demagnification lens, resulting in a full amplitude mask. The internal design of the density filter ensured a linear shift in light exposition during manufacturing, particularly affecting the smallest elements of the USAF test target. The customized density filter was later stacked above the positive USAF test target, creating gradual changes in phase across different regions. A second photosensitive film, placed beneath the stacked filter and positive USAF, recorded the customized phase test target. Illumination with a white LED source exposed the film to a maximum of 200 mJ/cm2 in areas with higher transmission, resulting in a thickness of approximately 700 nm. The exposed film underwent the D-19 developing and Kodak F-24 fixation processes, followed by bleaching with a potassium ferrocyanide bath to obtain a pure phase element. The result was the customized phase test target, as depicted in Fig. 2 b).
Fig. 2. Schemes of the elements required to build the proposed phase target: a) Specially designed linear filter. b) Stack of the customized filter and the positive USAF target to record the phase target.
3.2 Spatial phase sensitivity
Four recordings of each QPI technique are reconstructed to assess phase sensitivity using the customized phase target. The DHM system uses a 20× microscope objective (MO) with a 200 mm tube lens (TL) and a monochromatic 633 nm laser source for this experimental validation. In the case of the DLHM system, 633 nm laser illumination and a 5 µm pinhole are used with z = 2 mm and L = 10 mm. Both systems are equipped with a High-Resolution Raspberry Pi Camera sensor, capable of recording images with 3040 × 3040 square pixels of 1.55 µm pitch, yielding a full sensor size of 4.71 × 4.71 mm2. The same camera is employed in both systems to ensure consistency in the phase sensitivity, eliminating potential differences caused by electronic discretization and focusing solely on the impact of the optical elements within each QPI method.
Figure 3 illustrates, in panels (a) and (c), wrapped phase reconstructions from DLHM and DHM, respectively. The unwrapped phase maps, attained using [59,60], are presented in panels (b) and (d). Ten profile lines are taken over the bar elements (only a few are indicated by black arrows in panels b and d of Fig. 3 and ten over the background phase level (indicated by orange dotted lines in panels b and d of Fig. 3. An average profile line is calculated for the ten black lines, and a separate average profile line is computed for the orange dotted lines. These two profile lines’ mean value and standard deviation are then determined. As a result, each image provides an average profile representing the elements and another the sample-free background, both accompanied by their respective uncertainties. These profiles and their statistics are presented in Fig. 4.
Fig. 3. Phase reconstructions of groups 3-6 of the customized USAF phase test target captured with DLHM (panel a and b) and DHM (panel c and d). The wrapped (panels a and c) and unwrapped (panels b and c) reconstructions are presented. The dashed orange lines represent the background profiles, and the black lines represent the profiles through the elements.
Fig. 4. Phase profiles of the DLHM (panel a) and DHM (panel b) reconstruction. The zoom-in square shows the mean background level (continuous blue line), the upper and lower uncertainty limits of the background (dashed green lines), the mean value of the first element (dashed red line), and the mean value of the second element (continuous red line).
The following procedure is implemented to properly gather phase sensitivity information from the average profile lines described previously. In Fig. 4, individual bars of the customized phase target are identified and labeled accordingly (first, second, and third elements). Subsequently, a single mean value is calculated for the first and second elements (red dashed lines and red continuous lines, respectively). This figure reports the background mean with the blue line and its uncertainty with dashed green lines. The uncertainty value is computed as the standard deviation of the background profile line.
The spatial phase sensitivity of the QPI methods is now quantified using the uncertainty of the background phase measurements [1]. The information regarding the tilted area of the sample is omitted in this assessment. In this experiment, for the DLHM system, a phase uncertainty of 0.19 radians is achieved, in contrast to 0.18 radians by the DHM system (dashed green lines in Fig. 4. Based on the obtained results, it is evident that the first element could not be distinguished from the background using either of the techniques. This is primarily because its average value falls within the uncertainty limits represented by the red dashed line in both cases. However, the situation differs for the second element. According to DHM measurements, this bar is successfully differentiated from the background. In contrast, DLHM yields a distinct outcome, as the second element remains undifferentiated. All the latter predictions can be visually examined in Fig. 3, panels b and d. The challenges discussed earlier regarding DLHM in accurately measuring phase values significantly contribute to the observed discrepancies. These limitations stem from the inherent characteristics of DLHM, encompassing factors like diffraction artifacts, an incomplete representation of the complex wavefield, and difficulties in adequately sampling the diffraction pattern, particularly at high frequencies. These challenges manifest as discrepancies in the resulting phase images, especially at the edges of the imaged objects.
Considering that the refraction index of the customized test target is 1.61, and the illumination wavelength, the minimum thickness change detected with each method using the customized phase test target is 31.37 nm (DLHM) and 29.72 nm (DHM). The obtained results are anticipated since the DHM system incorporates a higher level of specialized and high-quality elements, although at the cost of a reasonably expensive QPI solution.
3.3 Phase measurement accuracy
The bar with the higher thickness of element 6 of group 3 (the third element of Fig. 3) is selected to asses QPI measurement accuracy. To validate the phase and thickness measurements obtained from the DLHM and DHM systems, a Nanosurf Easyscan2 AFM is utilized. This device offers a scan area of 70 µm x 70 µm with lateral and vertical resolutions of 1.1 nm and 0.21 nm, respectively. Figure 5 presents the results of these measurements. The images provided by each technique are displayed in panels a (DHM), b (AFM), and c (DLHM). Ten profile lines have been used to assess phase accuracy. Some of them are marked in these panels for illustration purposes. The average profiles for each method are plotted in panel d. The blue line corresponds to the DHM average profile, the green line to the AFM average profile, and the red line to the DLHM average profile.
Fig. 5. Profile of group 3-6 thicker element measured with different techniques: a) DHM phase reconstruction. b) AFM image (ground truth data). c) DLHM phase reconstruction. The blue, green, and red lines represent the selected profile in each case, respectively. d) Comparison of the three selected profile lines.
When measured using the AFM, the highest point of the element exhibited a height of 644.1 ± 0.21 nm. The same point is then measured using the DHM system, resulting in a height of 664.9 ± 29.72 nm, and with the DLHM system, the height is measured at 618.6 ± 31.37 nm. Comparing these measurements with the AFM reference value, the DHM system showed a 3.22% error, while the DLHM system had a 4% error. Overall, the measurements obtained from the DHM system are closer to those of AFM. These results are consistent with the findings reported in the literature [58,61], validating the accuracy of the selected techniques as QPI methods with phase measurement errors in the order of tens of nanometers.
3.4 Spatial lateral resolution
In both techniques, the spatial lateral resolution is determined by identifying the smallest resolvable objects in the customized USAF phase test target. Since DLHM requires thin and weak scattered objects to be imaged, the customized phase target fulfills this need and allows proper lateral resolution assessment in this method. The results in Fig. 6 reveal that the DHM system correctly reconstructs objects down to elements 7-3 of the target (see panel a), corresponding to 161.0 line pairs per millimeter (lppm), or 3.1µm lateral resolution. The DLHM technique attains an inferior performance, achieving 90.5 lppm, corresponding to elements 6-4 (See Fig. 6(c)), 5.52µm in lateral resolution. The profile lines of elements that are resolvable (blue lines) and those that are not (green lines) are displayed in panels b (DHM) and d (DLHM) of Fig. 6. As illustrated in Fig. 6(c), the DLHM image exhibits significant diffraction artifacts in the background. These artifacts can be attributed to challenges in adequately sampling the diffraction pattern in DLHM, especially at high frequencies and for those that cannot be adequately captured due to imperfections, resulting in diffraction effects. This issue is particularly pronounced for samples of non-weak scattering objects. While this limitation in sampling may lead to low-quality images in some cases, causing a reduction in the quality of the resulting DLHM phase images, it is crucial to emphasize that this does not impede the proper assessment of the resolution achieved by the technique.
Fig. 6. Lateral resolution measurements. Phase reconstruction of the smallest groups of the customized phase target: a) imaged with the DHM and c) imaged with the DLHM. Panels b) and c) present a profile over the smallest group that can be resolved (blue lines) and the next group unsatisfactorily resolved (green lines).
Both the DHM and DLHM systems demonstrate the ability to resolve fine details and achieve spatial lateral resolutions consistent with their respective numerical apertures (0.40 for the MO of the DHM system and 0.22 for the geometrical numerical aperture of the DLHM system). While the DLHM technique offered an inferior lateral resolution than DHM, both techniques effectively discerned fine features in the imaged object in the order of a few micrometers (<10µm).
To thoroughly validate the proposed comparative analysis in this paper, a comparison of two QPI systems intentionally set to the same NA in the sample region has been conducted. One recording of a commercially available USAF test target is acquired for this experiment for each QPI method. The DHM system utilized a 10× MO with a 200 mm TL and a monochromatic 633 nm laser source, resulting in a configured NA of 0.13 for the imaging system. In the case of the DLHM system, 633 nm laser illumination and a 5 µm pinhole is used with z = 2 mm and L = 20 mm, leading to a configured NA of 0.10. Both systems are equipped with the previously mentioned High-Resolution Raspberry Pi Camera sensor. To align the NA of the QPI systems, a digital reduction of the NA of the DHM hologram must be implemented. As illustrated in Fig. 7(a), the conventional mask of the +1 diffraction order is adjusted to consider frequencies corresponding to the virtual 0.10 NA system. The modification involved transforming the original mask delimited by the green circle in panel a to the circle delimited by the purple line, ensuring a proportional adjustment based on the ratio 0.13:0.10. Figure 7(b) displays the resulting amplitude reconstruction of the hologram at 0.13, and Fig. 7(c) presents the resulting amplitude at 0.10. For this study, Fig. 7 has been selected for comparison with the DLHM reconstruction to assess spatial lateral resolution.
Fig. 7. Numerical NA reduction of a DHM hologram. The ratio 0.13:0.10 is used to change the size of the circular mask during the spatial filtering procedure (panel a). Panel b is the amplitude reconstruction at 0.13 NA, and panel c is the reconstruction at 0.10 NA.
The outcomes of the comprehensive spatial lateral resolution comparison between the QPI methods under identical NA and FoV conditions are depicted in Fig. 8. Panel a showcases the amplitude reconstruction of the USAF test target obtained by the DHM system, while panel b presents the corresponding FoV using the DLHM system. A qualitative assessment in the insets of panels a and b, along with a quantitative evaluation in the profile lines depicted in panels c (where elements 7-3 are accurately imaged) and d (where elements 7-4 are not retrieved by any method), elucidate that both QPI imaging methods deliver the exact spatial lateral resolution as theoretically anticipated. This comparison under controlled NA and FoV conditions enhances the findings’ reliability and affirms the QPI systems’ precision in achieving the expected spatial resolution.
Fig. 8. Results of the spatial lateral resolution comparison between the QPI methods under identical NA and FoV conditions. a) Amplitude reconstruction provided by DHM. b) Amplitude reconstruction provided by DLHM. c) Profiles lines of both methods for the 7-3 elements of the USAF test target and d) for the 7-4 elements.
4. Conclusion
This comparative study evaluates the performance of two Quantitative Phase Imaging methods: single-shot off-axis Digital Holographic Microscopy (DHM) and Digital Lensless Holographic Microscopy (DLHM), with a primary focus on spatial phase sensitivity, phase measurement accuracy, and spatial lateral resolution. Ground truth data from an Atomic Force Microscope validates the study's findings, highlighting the superiority of DHM over DLHM in QPI analysis. DHM demonstrates nearly identical phase sensitivity to DLHM, boasting a minimal 3.2% measurement error compared to DLHM's 4% in height measurement. DHM's achievement of a finer lateral resolution down to 3.1 µm outperforms DLHM's 5.52 µm. However, it is crucial to note that these results depend on the parameters selected for each system, which were established in this study considering typical configurations for both methods. As expected, both techniques achieved an equivalent spatial resolution performance when controlling both NA and FoV to be the same in a final experiment. The enhanced imaging performance of DHM regarding measurement accuracy and phase sensitivity comes with the trade-off of a more robust and expensive system. The selection between DHM and DLHM must carefully consider the application's requirements, balancing imaging performance, portability, and costs.
The convergence of these diffraction- and interferometric-based technologies becomes apparent as DHM, traditionally associated with laboratory setups, adapts to recent trends by making strides toward portable implementations. This evolution reflects the growing demand for versatile solutions that seamlessly combine the precision of established laboratory techniques with the flexibility required for on-the-go applications that lensless methods, such as DLHM, provide. The choice between DHM and DLHM depends on the specific requirements of the application at hand. DHM is the preferred choice for applications demanding high precision and reliability, albeit with a more substantial system. In contrast, DLHM excels in scenarios prioritizing portability and cost-effectiveness. This comparative study contributes valuable insights to the ongoing discourse on the nuanced selection of QPI methods, recognizing the diverse needs of researchers and practitioners across various scientific and industrial domains.
Funding
Ministerio de Ciencia, Tecnología e Innovación (SGR 21); Universidad EAFIT (100013404); Fonds Wetenschappelijk Onderzoek (11PGG24N).
Acknowledgments
Authors acknowledge the support provided by Vicerrectoría de Ciencia, Tecnología e Innovación from Universidad EAFIT, and Professor Mauricio Arroyave, Ph.D., for conducting the measurement in the Atomic Force Microscope (AFM) at Universidad EAFIT. Sofia Obando-Vasquez and Maria Lopera acknowledge the Minciencias Research SGR21 Jovenes Investigadores program for supporting the investigation labor of young researchers in the country. Maria Lopera acknowledges the Flemish Fund for Scientific Research (FWO) for supporting her research (11PGG24N).
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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