Digital holographic microscopy (DHM) is one of the most effective methods in imaging the weakly-scattering objects, such as small colloidal particles and most biological cells. Compared to phase contrast and differential interference contrast microscopy, DHM cannot only visualize but quantify these phase objects. In this work, a spiral phase modulated FINCH microscope was implemented. The core of the system is an in-line incoherent interferometer composed of a spatial light modulator (SLM) and a charge-coupled device. In order to enhance image contrast, the SLM was space-division multiplexed by a helical lens and a conventional lens. To study the properties of this vortex imaging system, the precise mathematical model of the Point Spread Function (PSF), which describes the intensity distribution in digital image of the system’s response to a point source, is determined for the first time from the view of wave optics. The experimental 2D PSF agrees well with that of simulated one. When the system is used for biological microscopic imaging the enhancement of edge contrast and the enlargement of field of view are obtained without loss of resolution.
© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Digital holographic microscopy (DHM) is a promising tool for obtaining a three-dimensional image of both amplitude and phase objects [1–4]. It has vast application in label-free biological cell detection, material surface measurement, dynamic 3D shape measurement and micro-optical elements detection [5–8]. In traditional digital holography, laser light is required to implement the hologram recording. Laser speckle noise will seriously interfere with the experimental results, this, however, is inevitable in coherent imaging, and there is still no good way to solve it by now. In recent years, new types of digital holography under incoherent illumination have appeared [9–11]. Among them, FINCH records holograms from incoherent light with a SLM and a charge-coupled device (CCD) [12,13]. The FINCH system is an essentially in-line incoherent interferometer. The spherical wave emitted from each point of a 3D project is split by the SLM into two beams that interfere with each other. The interfere pattern is the point source hologram, and the entire interference pattern recorded by CCD is created from incoherent summation of the point source holograms from each point source in an incoherently emitting object. The FINCH technique can be readily adapted to any standard optical imaging technique with relatively little alteration, such as telescope and microscopy [14–17].
Edge extraction is the main means of image processing and pattern recognition [18–20]. Spiral phase filter (SPF), as a new diffractive optical element, has capabilities to generate optical vortex beams with helical wavefronts [21–24], which can be used for achieving image edge enhancement and pattern recognition [25–27]. During last two decades, SPF has been widely used in many practical applications, such as spiral phase contrast microscopy [28–30], astronomical observation [31,32], and quantitative imaging [33–35], etc. In subsequent research, the SPF was introduced to in-line digital holography based on the optical vortex phase-shifting method . Recently, Petr Bouchal and Zdeněk Bouchal  proposed a spiral contrast imaging method from standard FINCH by optical spiral recording, in which the SLM is multiplexed by a SPF and a spherical wave. The edge enhancement result is demonstrated on amplitude objects using an LED light source. This shows that the imaging characteristics of spiral FINCH system is different from those of traditional FINCH. But in , the imaging characteristics of the spiral FINCH was qualitatively described by analogy with those of traditional FINCH, and had not been analyzed theoretically. The precise mathematical description of the spiral PSF and the imaging effect of the system on the phase objects were also not given.
In this paper, a precise mathematical model of a spiral FINCH has been established based on wave optics, in which the SLM is space-division multiplexed by a helical lens and a conventional lens. The helical lens is a combination of a SPF and a thin lens. The point source hologram, PSF and the reconstruction distance of the system are obtained, which are different from those of traditional FINCH. The experimental point source hologram and PSF are consistent with those of computer simulation. When the system was used for imaging biological cells the effects of edge contrast enhancement and field of view (FOV) enlargement are obtained.
2. System analysis
Figure 1 shows schematic of the incoherent digital holographic microscopy system. A white-light source illuminates a 3D object, and the reflected light from the object is collected by an objective, and then propagated through a lens L and a SLM. The interference occurs on the plane of the CCD.
In order to evaluate the imaging quality of this system, we need to get the system’s PSF, which describes the intensity distribution in digital image of the system’s response to a point source. The SLM is space-division multiplexed by a helical lens and a conventional lens, whose reflection function can be described as the form
where λ is the working wavelength. αj (j = 1, 2, 3) are constant phase shifts, which can be used to eliminate the zero-order and twin image, B and B’ are constants, φ is the azimuthal angle on the SLM plane. The first item of Eq. (1) represents a conventional lens with focal length fd1, and the second item represents a helical lens which is a combination of a SPF with topological charge m, which denotes the winding number of the spiral, and a thin lens with focal length fd2. When the parameter m is zero, the system works in the dual lens FINCH mode, we call it the S-Pattern. For other values of m, we call it the V-Pattern.
The system consists of two parts, a microscope objective (MO) and a SLM-based interferometer. A point source located at S (0, 0,-zo) would be imaged by the objective lens to the point P (0, 0,-zs), a distance zs from a spherical positive lens, with f0 focal length, induces a diverging spherical wave on the lens plane with the form ofEq. (2) can be written as
Right after the SLM, with the reflection function given in Eq. (1), the complex amplitude is
Finally, in the CCD plane at a distance zh from the SLM, the complex amplitude is
From Eq. (9) we can see that the point source hologram has a helical wave-front structure with azimuthal angle θ and topological charge m. There is a phase singularity in the beam center, where the phase is uncertain and the light intensity remains zero because of destructive interference of the helical wave fronts. Consequently the reconstructed result shows a hollow point image.
Using a common computation routine of phase stepping, For each loading pattern, three different holograms with a different phase angle of 0°, 120° and 240° are captured and superimposed in the computer, such that the result doesn’t contain the zero-order and twin image.12]. The PSF of the spiral FINCH Ipsf can be reconstructed from IF by calculating the Fresnel propagation formula as
For a general 3D object g (x, y, z), the reconstructed image is an integral of the entire PSF given by Eq. (12), over all object intensity g (x, y, z), as follows
3. Experimental results
Schematic of the microscopic spiral imaging system based on FINCH is shown in Fig. 2. The phase masks of S and V (with topological charge m = 1) pattern are shown in the inset of Fig. 2. To get a quasi-monochromatic spatially incoherent illumination, a band pass filter with a peak wavelength of 633 nm and a bandwidth (FWHM, full width at half maximum) of 20 nm is positioned after the incoherent light source. The tested object is a USAF1951 resolution target, imaged by a 20 × , 0.4NA objective with a working distance of 5.9mm. The SLM is phase only, Holoeye Pluto, 1920 × 1080 pixels, 8μm pixel pitch. The distance between the collimation lens L (with a focal length of f0 = 250mm) and the SLM is d = 140mm. The direction of the polarizer is adjusted to the best position since the SLM is polarized-dependent. Both S pattern and V pattern have the same focal length of fd1 = 375mm and fd2 = 385mm. For the purpose of getting a relatively perfect overlapping of interfering beams, the SLM-CCD (Hamamatsu Digital Camera C8484-05, pixel size σc = 6.45μm, 1344 × 1024 pixels array) distance zh is 485mm. The superimposed complex valued holograms are digitally reconstructed in the computer. A small circular aperture with diameter of 20μm illuminated by xenon lamp (CEL-TCX250, 250W) is recorded by the system shown in Fig. 2 in V pattern. The simulated point source holograms with phase shift of 0°, 120° and 240° are shown in Figs. 3(a)-3(c), and the corresponding recorded holograms are shown in Figs. 3(e)-3(g). Considering the response sensitivity of the CCD, the simulated and recorded holograms are consistent. Figures. 3(d) and 3(h) show, respectively, the point spread functions from simulated and recorded data. Both results are consistent with each other very well, which verifies the correctness and effectiveness of the spiral imaging model in this paper.
In order to verify the performance of the system on the edge contrast enhancement of the objects, two groups of experiments are carried out on the setup illustrated in Fig. 2. The experimental results of resolution target are shown in Fig. 4. Figures. 4(a) and 4(c) are the reconstructed images of S and V pattern, respectively. Comparing with the reconstructed image of S pattern, the image of V pattern shows an obvious edge contrast enhancement. The reason is that incoherent object can be regarded as a collection of many point sources, each point source is modulated by spiral FINCH system and reconstructed into a hollow point image, and thus the edge information of incoherent object is extracted due to the superposition of all hollow point images. Figures. 4(b) and 4(d) show the part magnified image of the yellow box area in Figs. 4(a) and 4(c), which demonstrate that the resolution of system could be 512 lp/mm. The edge contrast of the two pictures can also be seen in Fig. 4(e), in which the normalized intensity profiles of the identical area from Figs. 4(a) and 4(c) are depicted by the red and blue line. Then the contrast experiments are conducted on the stained and unstained biological cells. Figures. 5(a) and 5(b) show reconstructed images of stained onion cells in S and V pattern, respectively. To verify the imaging ability of the system to phase objects, another experiment using fresh human blood lymphocytes as imaging object is carried out in the system. The corresponding results of S and V pattern are shown in Figs. 5(c) and 5(d). As can be seen from the experimental results in Fig. 5, in addition to the obvious edge contrast enhancement effect, the more interesting phenomenon is that the V mode can achieve a larger FOV at the same resolution compared to the S mode, which is important for a microscopic imaging system.
This paper has presented a detailed theoretical analysis of the imaging properties of the spiral FINCH system, which is composed of a SLM and a CCD camera. It should be noted here that the SLM isn’t indispensable, as a beam splitter and phase shift element, other cheap devices can be used instead. A precise mathematical model of the spiral imaging system has been established, in which the SLM is multiplexed by a helical lens and a conventional lens. The point source hologram, PSF and the reconstruction distance of the system are obtained, and the experimental point source hologram and PSF are compared with computer simulation and found to be in good agreement. When the system is used for imaging biological cells, the edge contrast enhancement effect and larger FOV are obtained without loss of resolution. In contrast to previous investigations of holographic microscopy, in addition to achieving edge contrast enhancement, the spiral phase modulated FINCH microscope system can reach balance between high resolution and large FOV. This effect can be used to record a series of pure phase samples such as label free living cell or intracellular tissue, which are commonly at most faintly visible in bright field mode.
National Science Foundation of China (NSFC) (61505178, 61307019, and 11504333); Natural Science Foundation of Henan Province of China (18A140032, 15A140038, and 16A140035).
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