Common-path laser interferometer

Qu, Xinghua; Wang, Lihua; Fu, Yanjun

doi:10.1364/ol.34.003809

Cited by 25 publications

(10 citation statements)

References 6 publications

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“…Depending on the sign convention adopted for m, the negative sign may or may not appear in Eq. (1). The important point is that ∆φ is independent of the incident angle (and wavelength), but dependent on m. In Fig.…”

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confidence: 92%

“…The end result is that both the p-and s-polarized beams have no phase change resulting from the displacement of the grating when they reach the polarizer P. One of the mistakes made in Refs. [1][2][3] is that the diffraction order numbers for both beams at both points A and B were set to +1. We set up the simple common-path interferometer to confirm our prediction.…”

mentioning

confidence: 99%

“…1 of Refs. [1][2][3], the s-and p-polarized beams are shown in solid and dashed lines, respectively. They share common paths but are drawn laterally shifted for clarity.…”

mentioning

confidence: 99%

“…The differences from the corresponding values used in the experiment reported in Refs. [1][2][3] are nonessential. As expected, the interferometer was very stable because of its high degree of common path.…”

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confidence: 99%

“…Our theoretical analysis and our experimental test cast doubt on the experimental results in Refs. [1][2][3].…”

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confidence: 99%

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Phase invariance in a recently proposed common-path laser interferometer

Feng¹,

Li²,

Zeng³

2012

中国光学快报

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This study shows that the principle of a recently proposed common-path laser interferometer containing a planar grating is nonexistent and apparently caused by a mathematical derivation error. Both p-and s-polarized beams in the proposed setup experience once the +1st-order diffraction and once the -1st-order diffraction by the grating. As a result, the phase of each beam remains unchanged and the interference fringes formed by the two beams are not expected to move when the grating is translated in the grating vector direction. We perform an experiment to confirm this prediction. Both our analysis and experimental observation cast doubt on the experimental results of the authors who proposed the interferometer.OCIS codes: 120. 3180, 120.3940, 230.19503180, 120.3940, 230. , 280.3340, 050.1950 In several recent publications, Qu et al. [1−3] proposed a common-path laser interferometer for displacement measurement. We point out that their analysis contains an error, rendering the principle of their displacement measurement nonexistent and their experimental results questionable.The optical phase of a beam diffracted from a grating changes by ∆φ after the grating is moved a distance ∆x in the grating vector direction, andwhere m is the diffraction order number and K = 2π/d, with d being the grating period. This formula can be proven based on the grating theory (Ref.[4]) or by considering the Doppler effect when the grating is moved and integrating the phase change caused by the frequency shift over the time of displacement. Depending on the sign convention adopted for m, the negative sign may or may not appear in Eq. (1). The important point is that ∆φ is independent of the incident angle (and wavelength), but dependent on m. In Fig. 1, which is essentially the same as the Fig. 1 of Refs. [1-3], the s-and p-polarized beams are shown in solid and dashed lines, respectively. They share common paths but are drawn laterally shifted for clarity. In research papers and textbooks different ways of writing the grating equation exist, and different sign conventions for the angles of incidence and diffraction, as well as for the diffraction order number m are used. However, as long as a set of conventions is used consistently, the diffraction order numbers at points A and B have the same absolute value but opposite signs. The sign difference is also easy to understand with the Doppler effect interpretation, wherein the light frequency is upshifted at one point (A or B) and downshifted at the other (B or A) by an equal amount for a given grating movement direction. The end result is that both the p-and s-polarized beams have no phase change resulting from the displacement of the grating when they reach the polarizer P. One of the mistakes made in Refs. [1][2][3] is that the diffraction order numbers for both beams at both points A and B were set to +1. We set up the simple common-path interferometer to confirm our prediction. A 632.8-nm wavelength He-Ne laser was used as the light source, and the grating line density was 1 74...

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confidence: 92%

mentioning

confidence: 99%

“…1 of Refs. [1][2][3], the s-and p-polarized beams are shown in solid and dashed lines, respectively. They share common paths but are drawn laterally shifted for clarity.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

“…Our theoretical analysis and our experimental test cast doubt on the experimental results in Refs. [1][2][3].…”

mentioning

confidence: 99%

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Phase invariance in a recently proposed common-path laser interferometer

Feng¹,

Li²,

Zeng³

2012

中国光学快报

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Digital Holographic Microscopy

Kim¹

2011

Digital Holographic Microscopy

103

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A traditional microscope is not capable of imaging phase object or three dimensional object. Computational Microscopy is proposed to address these two limitations. In Computational Microscopy, the sample is under coherent illumination and the intensities of the diffracted light are recorded by a detector system (CCD camera in most cases). The recorded information is then numerically processed by computer to retrieve the complex field scattered by the object from which the quantitative properties of the object are reconstructed. Three dimensional imaging via Computational Microscopy is performed by illuminating the semi-transparent object from multiple directions and solving the inverse scattering problem via techniques of Optical Diffraction Tomography(ODT).Digital holographic microscopy(DHM) discussed in this thesis is a synthetic implementation of the Computational Microscopy and employs phase-shifting digital holography for phase retrieval. Different experimental schemes were tested and three numerical back-propagation methods were implemented for back-propagating the complex wave from measurement plane to near field. The most emphasized part of the thesis is the research in the algorithms for ODT. An inverse scattering algorithm based on distorted wave approximation for the geometry of ODT is introduced. We implement the algorithm to two Optical Diffraction Tomography configurations: free space and cylindrical symmetric background. For free space case both near field and far field inverse scattering problems are studied. For cylindrical symmetric background inverse scattering based on Distorted Wave Born Approximation and Distorted Wave Rytov Approximation are discussed and compared via computer simulation. In addition, an inverse scattering algorithm based on ray tracing is derived based on the similar idea. Experimental results are presented in which we have successfully reconstructed transmission functions of 2D semi-transparent objects and refractive index profile of a step index optical fiber.

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