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Abstract
Quantitative phase imaging (QPI) of biological cells and tissues is an important technique useful in the determination of many biophysical parameters such as morphology, refractive index, thickness, cell dry mass, hemoglobin concentration, etc. Off-axis digital holography has been ideal for the QPI of microscopic specimens, but it has lower temporal stability compared to on-axis and common path digital holographic microscopes, which offer higher temporal stability. In this paper, we present a very simple, easy to align yet highly stable common path digital holographic microscope based on a Fresnel biprism interferometer. The system uses a biprism to divide the incoming beam into reference and object beams without the loss of optical power, unlike diffraction phase microscopy. Two methods are proposed, one by utilizing the spatial filtering mode and the other by the self-referencing mode. It offers the advantage that the reference beam can be easily created simply by translating the object in the focal plane of the microscopic objective or by spatially filtering one of the object beams in the Fourier domain. The proposed setup offers no power loss and a high phase stability of approximately 0.006 rad (6 mrad) without using any vibration isolation. The experiments on industrial and biological samples are reported demonstrating its application both for static and dynamic samples.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Most of the biological specimens are transparent in nature thereby making their imaging difficult under a bright field microscope. Digital holographic microscopy (DHM) has been developed as a powerful and accurate measurement technique, which provides us with amplitude and phase information of the transparent samples simultaneously [1–4]. The technique is advantageous due to its non-invasive, high resolution and wide field of view capability [5]. DHM can be implemented in two modes off-axis and in-line configurations. Off-axis DHM can be achieved either by Michelson or Mach-Zehnder type setups. The off axis DHM geometry initiates independent paths for the reference and object beams and passing through separate set of optical elements. Because of two widely separated paths this configuration becomes very sensitive to environmental vibrations, fluctuations, generate large phase noise thus resulting in low spatial and temporal stability [6,7]. The photon shot noise is often the limiting factor in interferometric microscopy measurements and by using state-of-the-art CCD camera with million-level electrons full well capacity can significantly reduce shot noise [8]. But cooled CCD cameras are expensive. Further off-axis DHM is not suitable for QPI of dynamic samples.
In recent years common path interferometers has been widely used due to its robustness and high stability [2,8]. In common path interferometers both the reference and object beams travel approximately the same path thus making them less sensitive to environmental vibrations and noise. Although being highly stable the common path interferometers deals with the shortcoming of generating twin images of the specimen. This shortcoming can be overcome depending on the method of generation of the reference beam. The first method involves the usage of spatial filtering in order to generate reference beam from the two object beams [6,7,9–11]. In [6] the author has employed a pinhole in the Fourier plane in combination to τ interferometer, which is a Michelson configuration. In [12,13] the authors have employed grating to generate the two beams and spatially filtered in the Fourier domain to obtain reference beam from one of the object beams. The use of grating leads to a great deal of power loss as only 0th and 1st diffraction orders are utilized [14–16]. In [16] a diffraction grating is utilized to generate a reference beam that traverses a blank region of the sample in a common-path off-axis interferometry setup to obtain tomographic imaging. The other method of overcoming twin image problem is to use self-referencing technique [17–21]. In [20,21] the authors have employed a single beam splitter to split and combine a spherical wavefront while placing sample in half of the beam. In [7,18,22] the authors have employed a glass plate to generate two laterally sheared beams and spatial filtering of one of the beams to generate reference beam but disadvantage being that glass plate reflects only 4% of the incoming power leading to surplus optical power loss which is lost in transmission as only reflected light is used.
In this paper, we report the development of a highly stable common path DHM, which has the capability of solving the twin image problem by both methods, mentioned earlier. The proposed setup makes use of a Fresnel biprism to generate two beams by dividing the incoming beam into two equal halves. The two generated beams are then interfered with the help of an asymmetric 4f imaging system in order to achieve sufficient fringe density on the image plane. The interference of two beams can be easily obtained using the present set-up without any hassle in the alignment of the two beams, as it is the simplest method of generating interference. The two beams have equal intensity, which is an essential requirement for interferometry. Further, the overlapping image problem in the present setup can be easily solved using spatial filtering in the Fourier domain. A much simpler and easy solution to the overlapping problem can also be done by self-referencing method. This can be easily achieved in our proposed set up as the Fresnel biprism divides the original beams into equal halves through the center of the beam without compensating on power such that one half contains object information while the other half does not. The advantage of the proposed setup is that it is easy to align, no power loss, high temporal stability due to its common path nature and can be used to image dense samples. Only the proposed setup can operate in any of the two possibilities at the same time, which is not possible with any other previously reported common path techniques.
2. Experimental setup
The schematic view of the experimental setup is shown in Fig. 1
Fig. 1 Experimental setup of proposed common path DHM using Fresnel biprism. OBJ is objective lens and L1, L2 and L3 are lenses of focal length 100mm, 100mm and 175mm.
3. Results and discussion
The hologram recorded by CCD camera is processed using Fourier fringe analysis technique (Fig. 2
). The recorded hologram was Fourier transformed and its 1st order peak was filtered out using a circular filter. Then amplitude and phase information was extracted from the image after taking inverse Fourier transform. A reference hologram was also recorded for each of the object samples for phase compensation and finally the phase was calculated by subtracting this background phase. The phase difference has been calculated using the formulae [7]where nc and nr are the refractive indices of the object and the surrounding medium, t is the thickness of the medium and λ is the wavelength used. Here, (nc - nr)t corresponds to the optical thickness of the specimen.The overlapping issue in our case can be easily resolved using spatial filtering or self-referencing method. In Fig. 3
Fig. 3 Overcoming the overlapping problem using (a) spatial filtering (inset 1) and (b) translating the sample (inset 2).
Fig. 4 (a) Hologram recorded of USAF 1951 resolution chart with spatial filtering and (b) reconstructed amplitude.
Fig. 5 (a) Hologram recorded of RBC sample with spatial filtering. (b) Zoomed in image of hologram and (c) reconstructed phase map.
The system proposed has high temporal stability due to its common path nature. The temporal stability of the set up was measured by recording a series of holograms with blank microscopic slide as sample. All the experiments have been performed without any vibration isolation. The hologram recording was done at the frame rate of 10 frames/sec for 15 secs. The phase difference was calculated for each of the frame initializing first frame as the reference frame. Standard deviation of the phase difference was measured for 10^4 random pixel locations giving us the mean standard deviation of 0.006 rad. Figure 6(a)
Fig. 6 Temporal stability of proposed setup. (a) Histogram of the standard deviation of phase difference of proposed setup with a mean variation of 0.006 rad. (b) Histogram of the standard deviation of phase difference of Mach-Zehnder setup with a mean variation of 0.2 rad.
In order to study the temporal versatility of our experimental setup for the measurement of dynamic samples we have studied the evaporation of acetone (Fisher scientific, (CH3)2CO Reagent grade) with time. The holograms were recorded using CCD camera at a frame rate of 10 frames/sec for a total of 4 seconds until the reagent completely evaporates. The refractive index of acetone as measured with Abbe refractometer (1.361) was used to calculate height of the droplets. The variation of height profile of droplets of acetone as it evaporates when exposed to air has been shown in Fig. 7
Fig. 7 Evaporation of acetone (CH3)2CO with time. 3D height profile of acetone at time instants 0.24s, 1.52s, 2s, 2.48s, 2.56s, and 3.12s. Color bar represents height in micrometers.
As discussed earlier that though introduction of pinhole in one of the beams overcomes the drawback of overlapping object but it is a bit difficult to align and tedious. A much simpler way is to translate the sample such that it occupies only half of the field of view of the objective lens while the other half acts as reference beam. This method has been described in Fig. 3 inset 2. To demonstrate this, the initial experiment was carried on a USAF 1951 resolution chart where the resolution chart lies in the right beam and the left beam acts as reference beam. Figure 8(a)
Fig. 8 (a) Hologram recorded of USAF 1951 resolution chart by translating the sample and (b) reconstructed amplitude.
Fig. 9 (a) Hologram recorded of RBC sample by translating the sample. (b) Zoomed in image of hologram (c) reconstructed phase image of red square in (b).
4. Conclusion
We have demonstrated a very easy to implement and align common path DHM using a Fresnel biprism. The object and reference beams are generated using spatial filtering and self-referencing methods. The holographic set-up is the simplest to align among all the common path configurations reported so far. The two beams that pass through the same set of optical elements and interfere in the camera plane to produce hologram with a temporal stability of 0.006 rad without any vibration isolation. The temporal stability of the present set-up is much better than the off-axis configuration. Therefore, the proposed DHM is most suitable for QPI of dynamic samples such as cell membrane fluctuations and QPI of micro-fluidic channels. Further, the setup is compact and robust which can be easily deployed for field studies without any vibration isolation. Experiments with industrial and biological samples have been shown in the two proposed arrangements namely by use of spatial filtering and translation of the sample. Though it suffers with disadvantage of offering only half field of view, offers the advantage of being simple, amenable, high temporal stability with no power loss.
Funding
Department of Science and Technology (IDP/MED/14/2016/General).
Acknowledgments
The authors are thankful to the Department of Science and Technology for funding the project no. IDP/MED/14/2016/General.
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