Application of Fresnel diffraction from a phase step to the measurement of film thickness

Tavassoly, Mohammad Taghi; Haghighi, Iman; Hassani, Khosrow

doi:10.1364/ao.48.005497

Cited by 31 publications

(23 citation statements)

References 8 publications

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“…Experimental results show that the 4 quadrants are producing the desired linearly and circularly polarized beams, as can be derived from the intensity transmission for each analyzer orientation. For instance, when the linear analyzer is set vertical or horizontal, a uniform intensity is obtained (although dark lines may appear on the quadrant edges whenever a phase discontinuity is created in the transmitted pattern [10,11]). These experimental results show that we can create a two-dimensional polarization map with a single pass through the SLM.…”

Section: Single Modulation Theory and Experimental Resultsmentioning

confidence: 99%

Complete polarization control of light from a liquid crystal spatial light modulator

et al. 2011

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We present a method to generate complete arbitrary spatially variant polarization modulation of a light beam by means of a parallel aligned nematic liquid crystal spatial light modulator (SLM). We first analyze the polarization modulation properties in a transmission mode. We encode diffraction gratings onto the SLM and show how to achieve partial polarization control of the zero order transmitted light. We then extend the technique to a double modulation scheme, which is implemented using a single SLM divided in two areas in a reflective configuration. The polarization states of the transmitted beam from the first pass through the first area are rotated using two passes through a quarter wave plate. The beam then passes through the second area of the SLM where additional polarization information can be encoded. By combining previously reported techniques, we can achieve complete amplitude, phase and polarization control for the diffracted light that allows the creation of arbitrary diffractive optical elements including polarization control. Theoretical analysis based on the Jones matrix formalism, as well as excellent experimental results are presented.

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Section: Single Modulation Theory and Experimental Resultsmentioning

confidence: 99%

Complete polarization control of light from a liquid crystal spatial light modulator

et al. 2011

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“…[23-27, 34-36, 39] in addition of the present paper). [23] and can be used in order to manufacture a nanopositioner based on FD from 2D PS. (Central panel) A typical 1D phase step with variable height [35,36] which can be used to manufacture a wavemeter, or spectrometer.…”

Section: Conclusion Discussion and Outlookmentioning

confidence: 99%

“…However, based on our numerical simulation which is shown in subsection 2B and also based on our experimental results which are shown in Tables 1 and 2 [which show that fitting method can provide thickness of thin films precisely], one can conclude that the fitting method based on FD from nano PS has the potential to become a highly valuable method for measuring the optical constants of materials, i.e., Ellipsometry based on FD from PS. [23] and can be used in order to manufacture a nanopositioner based on FD from 2D PS. (Central panel) A typical 1D phase step with variable height [35,36] which can be used to manufacture a wavemeter, or spectrometer.…”

Section: Conclusion Discussion and Outlookmentioning

confidence: 99%

“…(3) is a universal curve and one can always get the step height by plotting visibility versus incident angle and equating its slope with the slope of the relevant plotted line in Fig. (3), [23]. Using this technique, i.e., the visibility method, the step heights in the range of few tens nanometers up to several millimeters have been measured [23,24].…”

Section: Theoretical Approach a Theoretical Formulation Of Fd From Amentioning

confidence: 99%

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Measurement of thickness of thin film by fitting to the intensity profile of Fresnel diffraction from a nanophase step

2018

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Diffraction of light beams from the phase steps due to the abrupt/sharp changes in the boundary of step leads to Fresnel fringes whose visibility and intensity profile depend on the change of the step height or light incident angle. The visibility has been utilized in measurements of different physical quantities. In this paper, for the first time to our knowledge by introducing the fitting method as a fast method we show that by fitting the theoretical intensity distributions on the experimental intensity profiles of the light diffracted from a step at different incident angles, one can specify the step height with few nanometers precision. In addition, we show that this approach provides accurate film thickness in a broad range of thicknesses using modest instrumentation. Furthermore, based on Fresnel diffraction from phase step we have manufactured and trademarked an optical device for measuring thickness of thin films.

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“…However, for accurate measurement, usually high-quality optics and, in many cases, sophisticated instrumentation are required [9]. But recently the Fresnel diffraction from phase steps have been studied rather in detail [10][11][12], and it has been shown that, by modest optics, the effect can be applied to accurate and reliable measurements of refractive index [13], film thickness [14], index profile of optical fiber [15], and nanometer displacements [16]. In our previous work, applying Fresnel diffraction from the edge of a transparent plane-parallel plate, we measured the refractive indices of transparent solids and liquids [17].…”

Section: Introductionmentioning

confidence: 99%

Applications of Fresnel diffraction from the edge of a transparent plate in transmission

et al. 2012

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When a transparent plane-parallel plate is illuminated at the edge region by a quasi-monochromatic parallel beam of light, diffraction fringes appear on a plane perpendicular to the transmitted beam direction. The sharp change in the refractive index at the plate boundary imposes an abrupt change on the phase of the illuminating beam that leads to the Fresnel diffraction. The visibility of the diffraction fringes depends on the plate thickness, refractive index, light wavelength, and angle of incidence. In this report we show that, by recording the visibility repetition versus incident angle, one can measure the plate refractive index, its thickness, and light wavelength very accurately. It is also shown that the technique is indispensable for specifying color dispersion in plate shape samples. The technique is applied to the measurement of dispersion in a fused silica plate and the refractive indices of soda lime slides.

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Application of Fresnel diffraction from a phase step to the measurement of film thickness

Cited by 31 publications

References 8 publications

Complete polarization control of light from a liquid crystal spatial light modulator

Complete polarization control of light from a liquid crystal spatial light modulator

Measurement of thickness of thin film by fitting to the intensity profile of Fresnel diffraction from a nanophase step

Applications of Fresnel diffraction from the edge of a transparent plate in transmission

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