Investigation of Fresnel biprism interference from the perspective of information optics
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摘要: 菲涅耳双棱镜干涉在相衬成像和全息显微术中有重要应用。为了促进其应用，本文从信息光学角度研究双棱镜干涉，首先利用光场与脉冲响应函数之间的关系，理论导出了菲涅耳双棱镜干涉条纹强度公式，分析并讨论了狭缝缝宽及狭缝到双棱镜距离对菲涅耳双棱镜干涉条纹的影响，狭缝宽度大于0.1 mm时，干涉条纹分辨率变差。接着给出了改变狭缝宽度（变化量为0.08 mm）和改变狭缝到双棱镜的距离（从8 cm变化到12 cm）的实验结果，理论分析和实验结果一致。该结果有助于促进菲涅耳双棱镜干涉在相衬成像等领域的应用。Abstract: It was recently found that Fresnel biprism interference has applications in phase contrast imaging and digital holographic microscopy. In order to promote these applications and understand their physics, Fresnel biprism interference is investigated in information optics. Firstly, the relationship between optical field and impulse response function is analyzed, then a formula for measuring the intensity of Fresnel biprism interference is derived. The influence of single-slit width and the distance between the single-slit and the biprism on the quality of an interference pattern are theoretically analyzed from the perspective of information optics. It was found that the resolution of the interference fringe becomes worse as the slit-width exceeds 0.1 mm. Then, by changing the slit width(by 0.08 mm) and the distance between the biprism and the slit(by 8 cm to 12 cm) in accordance with the developed experiment scheme, the observed experimental results are consistent with theoretical analysis. These results could help deepen our understanding of phase contrast imaging based on Fresnel biprism interference.
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图 2 不同缝光源宽度条件下的菲涅耳双棱镜干涉条纹，右列为左列对应的一维图
Figure 2. Interference fringes of Fresnel biprism under different widths of slit light source, (Left Column:Two-Dimensional Patterns, Right Column:the corresponding 1D fringes)
图 3 不同z1(狭缝到双棱镜的距离)条件下的干涉条纹，右列为左列对应的一维图
Figure 3. Interference fringes of Fresnel biprism under different z1(the distance between single-slit and biprism), (Left Column:Two-Dimensional Patterns, Right Column:the corresponding 1D fringes)
图 4 干涉条纹强度分布.右列为左列对应的一维图，(a)含有常数项, (b)不含常数项
Figure 4. Intensity distributions of the interference fringe, Left Column:Two-Dimensional Patterns, Right Column:the corresponding 1D fringes. (a) and (b) are the corresponding results for that including the constant item and neglecting constant item of intensity, respectively
图 5 干涉条纹图:(a)合适狭缝宽度; (b)狭缝宽度增加0.02 mm; (c)狭缝宽度增加0.08 mm
Figure 5. Interference patterns, (a), (b) and (c) are the corresponding results at suitable slit-width, slit-width increasing by 0.02 mm and 0.08 mm, respectively
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