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Abstract
We present a novel stable quantitative phase measurement technique for extending the imaging area sensing with the capability of recording two wavelengths in a single shot. For this purpose, each wavelength is separated into three beams using a Fresnel bi-prism and they interfere in the CCD camera by a simple optic alignment. The final pattern created in the camera with the six beam contained both wavelengths information that their field of view is extended two times. The feasibility of this technique is experimentally demonstrated by dispersion measurement of silica beads using two wavelengths image of two different areas of silica beads with a single image sensor.
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1. Introduction
Interferometric microscopy is a wide-field, noninvasive, label-free, high resolution and fast 3D imaging technique which is characterized objects by sub-nanometer sensitivity [1–4]. In order to investigate rapid phenomena that take place in many process such as biological cells, methods for simultaneous acquisition of multiple interference patterns are required. Some quantitative phase microscopes employ Frequency domain multiplexing to capture more than two phase images in a single measurement [5–8]. Multiplexing methods have been proposed for real time monitoring of the thickness and the refractive index of a phase object as well as the dispersion characteristics of a sample by using multi-wavelength phase microscopy [9–11]. Phase unwrapping is another application of multiplexing to increase the measurable thickness or height of a sample. Recently, some novel techniques such as multiple-illumination [12] or multiple-wavelength [13,14] methods have been introduced that utilized Fourier domain multiplexing idea for different application of phase microscopy. Extending the FOV of a measurement have been an important issue in quantitative phase imaging system. Because of the trade-off relation between the resolution and the FOV in microscopy system, increasing the FOV of system while keeping enough resolution could be a bit of a challenge [15]. Recording many images by mechanically translating the sample or image sensor is a simple technique to extend the FOV of quantitative phase microscopy at the price of adding extra vibrational noise and decreasing the speed of measurement. An alternative method of increasing the FOV proceeds by taking many images simultaneously with a single detector array by using multiplexing algorithms [16]. Recently a technique based on the simultaneous recording two FOVs on a single arrayed detector was proposed that obtained highly stable fringe patterns by designing a quasi-common-path interferometer with a simple alignment. Due to the fact that the reference beam and sample beam travel through the same path, this system is less sensitive to environmental vibrations than conventional interferometers [17].
In this letter we report a system which contains both advantages of multi-wavelength and double FOV in a single shot. We utilize a Fresnel bi-prism [18–20] to make different path for each wavelength. The separation of paths makes different angles of final beams entered to the camera and consequently different spatial frequency recorded for each wavelength. In addition to the separation of wavelength, the beams belonging to different object areas are separated and modulated by Fresnel bi-prism. The two object beams come from bi-prism and the reference beam that comes from a tilted mirror are combined to form interference patterns on the detector array, and the phase information of the different areas of the sample is subsequently located in different peaks in the Fourier domain. In the current study, our dual-wavelength and double FOV phase imaging scheme was applied to simultaneously measure microspheres with 10 µm in diameter.
2. Materials and methods
The experimental setup is depicted in Fig. 1(a). The source of this system consist of two lasers operating at wavelengths of λ1= 632 nm and λ2 = 402 nm that are combined to a single beam by means of a beam splitter.
Fig. 1. Schematic of dual wavelength and doubled FOV microscopic system. (a) The side view of the system. (b) The top view of the system without reference beam.
The expanded and collimated light with about 1 cm in diameter is passing through a specimen, then a 20x achromatic objective lens in combination with a tube lens produce an image in the image plane of microscope. The location of samples has been adjusted so that the half of incident beam pass through samples and half does not touch sample and works as reference beam [15]. A Fresnel bi-prism with 1 degree angle and 25 cm2 in area is located in the image plane so that the part of beam that contains sample information will pass through it but the reference part without touching prism directly enter the camera by tilted mirrors as shown in Fig. 1(a). The pixel size of CCD camera is 4.65µm x 4.65µm, and sensor size is 1/2 inch. The focal length of lenses used in this setup is f1 = 30 cm and f2 = 60 cm. The top view of the setup after the Fresnel bi-prism has been represented in Fig. 1(b). To facilitate a better understanding of the light paths, the presentation of reference beam has been neglected in Fig. 1(b). The information of FOV1 pass through right face of bi-prism and the FOV2 pass through left face. Due to the dispersion property of the Fresnel bi-prism, the violet and red light separate in different angle and therefore make different spatial frequency for each wavelength in final interference pattern by q = (sin θ)/λ. Where θ is the angle between the beams interfere in the camera. Because of the incoherency between the red and violet beams, the final pattern consists of two interference pattern corresponding to each wavelength. The intensity pattern formed on the camera can be interpreted by:
Since two wavelengths enter the camera with different angles, the spatial frequency of the interference pattern for each color would be different. Therefore, the sample information for each wavelength modulate on separated frequency in Fourier domain by:
Fig. 2. (a) The final pattern formed by interfering six beams. (b) The Fourier transformation of pattern.
In this experiment 10 µm silica beads immersed in ethylene glycol was considered for doubling the FOV of dual wavelengths measurement. The system was utilized for the dispersion measurement of the silica beads. Figure 3 represents the phase images for two wavelengths and two FOVs obtained from single interference pattern. Figures 3(a) and 3(b) demonstrate the phase image for λ1 = 632 nm and λ2= 402 nm in the first field of view. Two images were obtained by filtering two peaks corresponding to exp(iΦ1)red and exp(iΦ1)vio . It can be seen in the figures that the maximum phase difference between bead samples and the medium for the red beam is around 2.5 ± 0.1 radian while it is around -4.5 + 0.1 for violet beam.
Fig. 3. The phase images of silica beads immersed in ethylene glycol corresponding to the FOVs and wavelengths. (a) FOV1 and λ1 (b) FOV1 and λ2 (c) FOV2 and λ1 (d) FOV2 and λ2.
Based on the databases, the refractive indexes of the ethylene glycol are 1.431 for λ1 = 632 nm and 1.497 for λ2= 402.
The refractive indexes of silica bead in two wavelengths were obtained by Φ = (2π/λ)δnt . The measured refractive indexes were n(λ1) =1.456 ± 00.1 and n(λ2) =1.469 ± 00.1 that well agreed with the refractive index database of silica. Figures 3(c) and 3(d) illustrate the phase images for the second FOV in λ1 and λ2 respectively. These images are resulted from two peaks corresponding to exp(iΦ1)red and exp(iΦ1)vio. These two field of view of phase images for each wavelength can be interconnected manually in order to doubling the field of view.
The two wavelengths phase images in Fig. 3 can be used for many purposes of the multi-wavelength phase imaging such as avoiding the index-thickness ambiguity of the phase data, the characterizing of dispersion in samples, improving axial accuracy [21], or the phase unwrapping.
3. Conclusion
In this study, we proposed an optical scheme for extending the FOV of dual wavelength phase microscopy keeping the advantages of single shot measurement. This system is a common-path microscope that can acquire four phase shift in a single image. By using a Fresnel bi-prism, the combined two wavelength beam separated in four beam and interfere in the camera with different spatial frequency. Two reference beam without any incidence to the prism was directly irradiated to the camera and finally six beam interference pattern was recorded. Using Fourier domain multiplexing and filtering the information of each phases, four phase image were obtained from the interfrogram. The feasibility of the proposed technique was demonstrated by measuring the phase shift of silica beads immersed in ethylene glycol. The results represented that the technique capability for increasing the FOV while keeping the advantages of common-path dual wavelengths phase microscopy.
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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