Der-Chin Su’s research while affiliated with National Yang Ming Chiao Tung University and other places

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Publications (89)


Complex refractive-index measurement based on Fresnel's equations and the uses of heterodyne interferometry
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September 2013

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434 Reads

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2 Citations

Applied Optics

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Der-Chin Su

The phase difference between s and p polarization of the light reflected from a material is used for measuring the material's complex refractive index. First, two phase differences that correspond to two different incidence angles are measured by heterodyne interferometry. Then these two phase differ-ences are substituted into Fresnel's equations, and a set of simultaneous equations is obtained. Finally, the equations are solved by use of a personal computer by a numerical analysis technique, and the complex refractive index of the material can be estimated.

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Fig. 1. Schematic representation of the conventional polarization-selective substrate-mode volume hologram. In this structure, H I , H PBS , H OS , and H OP are actually transmission-type phase volume 
Fig. 2. Reconstruction geometry of the phase volume hologram: S, s -polarization field; P, p polarization field. In the case of normal incident, i . e . θ r 1 =0 ° , eqs. (2) and (3) can be reduced as 
Fig. 3. Schematic representation of the proposed polarization-selective substrate-mode volume hologram (I). In addition, in the same principle, we can properly choose the substrate with its refractive index equally that of the recording material ( n s = n f ). Under this condition, the light propagation details in Fig. 3 change as shown in Fig. 4. The light separated distance 
Fig. 4. Schematic representation of the proposed polarization-selective substrate-mode volume hologram (II). According to eqs. (1), (5), and (6), the relation between the diffraction efficiencies of s - and p components can be rewritten as 
Fig. 5. The relation of x v.s. diffraction efficiencies, η s and η p , considering θ r2 =85°. 

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Polarization-Selective Substrate-Mode Volume Holograms and Its Application to Optical Circulators

November 2011

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145 Reads


The schematic diagram of this method. TDL, tunable diode laser; EOM, electro-optic modulator; FG, function generator; BS, beam splitter; PBS, polarizing beam splitter; MO, microscopic objective; T, transparent plate; M, mirror; TS, translation stage; AN, analyzer; ID, iris diaphragm; PD, photodetector; PM, phase meter.
Four identification points in the interferometer.
The result of a data acquisition test of the phase meter.
The phase changes with the wavelength scanning from λ a to λ b in (a) a correct identification and (b) an incorrect identification with the phase wrapping condition.
The MO has a defocus error on the test plane.
High-accuracy thickness measurement of a transparent plate with the heterodyne central fringe identification technique

July 2011

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34 Reads

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5 Citations

Wang-Tsung Wu

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Wei-Yao Chang

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Der-Chin Su

In a modified Twyman–Green interferometer, the optical path variation is measured with the heterodyne central fringe identification technique, as the light beam is focused by a displaced microscopic objective on the front/rear surface of the test transparent plate. The optical path length variation is then measured similarly after the test plate is removed. The geometrical thickness of the test plate can be calculated under the consideration of dispersion effect. This method has a wide measurable range and a high accuracy in the measurable range.


Optimal sampling conditions for a commonly used charge-coupled device camera in the full-field heterodyne interferometry

April 2011

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19 Reads

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2 Citations

Optical Engineering

The processes to derive the associated phase of an interference signal from the data of a series of recorded frames are performed, and we find that the sampling frequency being lower than the Nyquist sampling rate can also be applied to the full-field heterodyne interferometry. Two optimal sampling conditions for a commonly used CCD camera are proposed based on the relation between the heterodyne frequency and the contrast of the interference signal under the condition that the phase error is set to be 0.05 deg.


Schematic diagram of the modified Twyman–Green interferometer.
Configuration of the heterodyne light source.
(a) Sampled interference signal as V < V π and (b) corresponding modified interference signal with lengthened period.
Refractive-index contour of the GRIN lens with this method.
Refractive-index contour of the same GRIN lens with our previous method.
Alternative method for measuring the full-field refractive index of a gradient-index lens with normal incidence heterodyne interferometry

December 2010

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17 Reads

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16 Citations

A linearly/circularly polarized heterodyne light beam coming from a heterodyne light source with an electro-optic modulator in turn enters a modified Twyman–Green interferometer to measure the surface plane of a GRIN lens. Two groups of periodic sinusoidal segments recorded by a fast complementary metal-oxide semiconductor camera are modified, and their associated phases are derived with the unique technique. The data are substituted into the special equations derived from the Fresnel equations, and the refractive index can be obtained. When the processes are applied to other pixels, the full-field refractive-index distribution can be obtained similarly. Its validity is demonstrated.


An alternative bend-testing technique for a flexible indium tin oxide film

December 2010

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31 Reads

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7 Citations

Displays

The two-dimensional refractive index distribution of a flexible indium tin oxide film deposited on a PET layer is measured before/after the bend-testing with an alternative technique based on Fresnel equations and the heterodyne interferometry. Their standard deviations are derived and they vary more obviously than the resistance variations measured in the conventional method. Hence the standard deviation of the refractive index can be used as the indicator to justify the durability of a flexible indium tin oxide film. The validity is demonstrated.


Full-field refractive index distribution measurement of a gradient-index lens with heterodyne interferometry

September 2010

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20 Reads

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6 Citations

Measurement Science and Technology

A light beam coming from a circular heterodyne light source with an electro-optic modulator is incident on a gradient-index lens obliquely. The reflected light passes through an analyzer and an imaging lens, and is recorded by a fast CMOS camera. A group of periodic sinusoidal segments recorded by each pixel is modified, and its associated phase is derived with a unique technique. The processes are applied to other pixels; the two-dimensional phase distribution can be obtained similarly. The estimated data are substituted into the special equations derived from Fresnel's equations, and the full-field refractive index distribution of the gradient-index lens can be obtained. This method has the merits of both common-path interferometry and heterodyne interferometry.


Improved technique for measuring full-field absolute phases in a common-path heterodyne interferometer

August 2010

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13 Reads

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4 Citations

When an asymmetric triangle voltage signal is applied to drive an electro-optic modulator, interference signals with two groups of periodic sinusoidal segments with different frequencies are obtained. An improved method is proposed to fit these two groups of segments, and their associated phases can be determined. The absolute phase can be obtained by subtracting the initial phase from the phases of these two groups. This technique is applied to all pixels, and the full-field absolute phase measurements can be achieved. The validity of this method is demonstrated.


Schematic diagram of this method. TDL, tunable diode laser; EO, electro-optic modulator; FG, function generator; BS, beam splitter; PR, prism; PBS, polarizing beam splitter; G, gauge block; W, wringing platen; M, mirror; TS, translation stage; AN, analyzer; D, photodetector; SW, switch; OSC, oscilloscope; PM, phase meter.
Signals display on the oscilloscope. The peak of the sine-wave signal shifts over one period from point A to point B, as the wavelength scans from λ 1 to λ 2 .
Result of a data acquisition test of the phase meter.
Method for gauge block measurement with the heterodyne central fringe identification technique

May 2010

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13 Reads

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2 Citations

In a modified Michelson interferometer, the top face of the wringing platen is first identified using the heterodyne central fringe identification technique. Then the reference mirror located in the other arm is moved by a precision translation stage until the top face of the tested gauge block is also identified with the same technique. The displacement of the mirror is exactly equivalent to the length of the tested gauge block. The measurable range of the interferometer relates to the maximum travel range of the translation stage and its uncertainty depends on the uncertainty of the heterodyne central fringe identification method and the resolution of the translation stage.


A method for measuring the geometrical topography of a Rockwell diamond indenter

December 2009

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25 Reads

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6 Citations

Measurement Science and Technology

Firstly, a Rockwell diamond indenter tip is tested at different angles and positions by using a scanning white light interferometer, and several image data are obtained. Then, these data are merged together to form the associated geometrical topography with the image stitching method. Moreover, both the tip radius and the cone angle can be obtained with the least-squares Gauss–Newton sphere and cone fitting algorithm. Its validity is demonstrated.


Citations (57)


... In the laboratory, spectroscopic methods [13] are often used. Spectroscopic methods mainly use light refraction [14], interference [15], diffraction [16] and other characteristics to measure solution concentration indirectly. Although the technology of these methods is relatively mature, this approach often needs complex experimental equipment and is expensive. ...

Reference:

A instrument for measuring solution concentration
Measurement of the concentration of a solution with surface plasmon resonance heterodyne interferometry
  • Citing Article
  • July 2003

Optical Engineering

... In this paper, we propose a new method for accurately measuring the geometrical thickness of a transparent plate by using the heterodyne central fringe identification technique [11]. In a modified Twyman-Green interferometer with a polarization beam splitter (PBS), a high-precision translation stage (TS) is used to displace the reference mirror in one arm and a long working distance MO is located with the test transparent plate in the other arm. ...

Central fringe identification using a heterodyne interferometric technique and a tunable laser-diode
  • Citing Article
  • July 1996

Optics Communications

... The authors concluded that aberrations adversely affect self-images, especially those located at higher-order Talbot planes; even the contrast inversion in fringes is observed. Toward resolving the issues stated above, researchers investigated gratings/structures other than the "linear," such as dual-field, evolute, spiral, triangular, and circular [25][26][27][28][29][30][31], for improved accuracy. ...

Moire Fringes by Two Spiral Gratings and Its Applications on Collimation Tests
  • Citing Article
  • January 1995

Chinese Journal of Physics

... Conventionally, the Jamin-Lebedeff interferometer uses orthogonal linear polarization states and is able to determine refractive indices of crystals and biological materials [3,6], improve the contrast in microscopic imaging [7,8] and measure refractive indices of metallic nanostructures [9]. Common-path interferometers exist that take advantage of circularly polarization states and that are able to measure not only conventional refractive indices [10][11][12], but also the circular birefringence, i.e. the difference (n L -n R ) [13]. However, an interferometer that can determine the circular-polarization (CP) dependent refractive indices n L and n R has, to the best of our knowledge, not been reported. ...

Measurements of material refractive index with a circular heterodyne interferometer
  • Citing Article
  • June 2005

Proceedings of SPIE - The International Society for Optical Engineering

... They are potentially easier to fabricate than the thin-film filters, and, when they are incorporated into planar configurations, alignment problems are greatly alleviated. [5][6][7][8][9] Most of these configurations involve two gratings, one grating for dispersing and separating wavelength channels and an output grating for coupling the light outward. In general, such grating-based configurations have either nonuniform throughput light efficiency among different wavelength channels or gradual roll-off rather than a cutoff spectral profile. ...

Novel substrate-mode grating structure for wavelength-division demultiplexing
  • Citing Article
  • October 1992

Proceedings of SPIE - The International Society for Optical Engineering

... Biological applications of ellipsometry include the measurement of the thickness of macaque retinal nerve layers [19], which was measured to be between about 20 µm and about 215 µm. A related technique called circular heterodyne interferometry uses the reflection of a rotating linear polarisation and detection of the angle of maximum transmission through an analyser to retrieve thickness and refractive index by measuring at two analyser angles [20]. Spectroscopic ellipsometry, combining measurements at multiple wavelengths, has been employed to determine the thickness and (by studying absorption bands) the chemical composition of silane films several hundred nanometres thick [21], as well as to measure the thickness and electric permittivity of nanometric tellurium layers and decananometric polypyrrole layers [22]. ...

Thickness and optical constants measurement of thin film growth with circular heterodyne interferometry
  • Citing Article
  • November 2005

Thin Solid Films

... In addition to the above several configurations, according to the optical path structure and the position of the microscope, the commonly used microscopic interferometry systems can be divided into three types: Michelson type [16][17][18][19], Mirau type [20][21][22][23][24] and Linnik type [25][26][27][28][29][30][31][32][33]. For example, Wiersma, J.T. used the Michelson microscopic system and synchronous phase sensor to realize high precision and repeatable measurement of common vibration [19]; Schmit, J. proposed an improved Mirau interferometer, which can generate orthogonally polarized output beams, and can obtain better fringe contrast by introducing achromatic phase shift [21]; Somekh, M.G. realized a plasmon microscope with sub-micron resolution by using the Linnik interferometer with speckle illumination [26]; Li, X.D. of Tsinghua University measured the thermal deformation of copper microbridges with different sizes (the maximum size is 2175 µm × 1009 µm) in real time using the Linnik microscopic interferometry system, and the accuracy reached submicron level [33]. ...

Nano-roughness measurements with a modified Linnik microscope and the uses of full-field heterodyne interferometry
  • Citing Article
  • December 2008

Optical Engineering

... Although the relative thickness and the refractive index of the sample can be obtained directly, it takes a long time to finish a whole testing or it is very difficult to adjust the optical components precisely. In recent years, the He-Ne laser is often used as the laser source in the heterodyne interferometry [7][8][9], and the light beam is often incident on the front surface and reflected by the sample in such an interferometer system. So only the related information of the surface profiles of the sample can be obtained. ...

Alternative method for measuring both the refractive indices and the thickness of silver-halide holographic plates
  • Citing Article
  • May 2005

Optical Engineering

... For convenience, the +z axis is set as the light propagation direction and the +x axis is set as perpendicular to the paper plan. When the circularly polarized heterodyne light source that consists of a tunable laser, an electro-optic modulator (EO) (with fast axis lying at 45°), a function generator FG, linear voltage amplifier (LVA), and a quarter wave plate Q (with the fast axis lying along the xaxis), as shown in Fig. 2 [14,15], passes through a cholesteric liquid crystal cell with a thickness of d, its Jones vector E 1 of electric field can be written as ...

Simple method for measuring the extraordinary and ordinary indices of quartz plates
  • Citing Article
  • October 2001

Optical Engineering