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Research Papers

Description and Evaluation of a Simplified Model to Simulate the Optical Behavior of an Angle-Resolved Scattered Light Sensor

[+] Author and Article Information
François M. Torner

Institute for Measurement
and Sensor-Technology,
Technical University Kaiserslautern,
Gottlieb-Daimler-Str., Building 44, Room 221,
Kaiserslautern, Rhenania-Palatinate 67663,
Germany
e-mail: torner@mv.uni-kl.de

Gerhard Stelzer

Institute for Measurement
and Sensor-Technology,
Technical University Kaiserslautern,
Kaiserslautern, Rhenania-Palatinate 67663,
Germany
e-mail: stelzer@mv.uni-kl.de

Lukas Anslinger

Institute for Measurement
and Sensor-Technology,
Technical University Kaiserslautern,
Kaiserslautern, Rhenania-Palatinate 67663,
Germany
e-mail: anslinger@mv.uni-kl.de

Jörg Seewig

Professor
Institute for Measurement
and Sensor-Technology,
Technical University Kaiserslautern,
Kaiserslautern, Rhenania-Palatinate 67663,
Germany
e-mail: seewig@mv.uni-kl.de

Contributed by the Manufacturing Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received March 7, 2016; final manuscript received July 27, 2016; published online January 30, 2017. Assoc. Editor: Jan C. Aurich.

J. Comput. Inf. Sci. Eng 17(2), 021003 (Jan 30, 2017) (15 pages) Paper No: JCISE-16-1881; doi: 10.1115/1.4034386 History: Received March 07, 2016; Revised July 27, 2016

Scattered light sensors are optical sensors commonly used in industrial applications. They are particularly well suited to characterizing surface roughness. In contrast to most geometric measuring devices, a scattered light sensor measures reflection angles of surfaces according to the principle of the so-called mirror facet model. Surfaces can be evaluated based on the statistical distribution of the surface angles, meaning the gradients. To better understand how the sensor behaves, it is helpful to create a virtual model. Ray-tracing methods are just as conceivable as purely mathematical methods based on convolution. The mathematical description is especially interesting because it promotes fundamental comprehension of angle-resolved scattered light measurement technology and requires significantly less computation time than ray-tracing algorithms. Simplified and idealized assumptions are accepted. To reduce the effort required to simulate the sensor, an attempt was made to implement an idealized mathematical model using Matlab® to be able to quickly generate information on scattered light distribution without excessive effort. Studies were conducted to determine the extent to which the results of modeling correspond to the transfer characteristics of a virtual Zemax sensor, on the one hand, and with the measurement results of the actual scattered light sensor, on the other hand.

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References

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Seewig, J. , Damm, T. , Frasch, J. , Kauven, D. , Rau, S. , and Schnebele, J. , 2009, “ Reconstruction of Shape Using Gradient Measuring Optical Systems,” Fringe 2009, W. Osten , and Kujawinska, M. , eds., Springer, Berlin, pp. 1–7.
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Trost, M. , Herffurth, T. , Schmitz, D. , Schröder, S. , Duparré, A. , and Tünnermann, A. , 2013, “ Evaluation of Subsurface Damage by Light Scattering Techniques,” Appl. Opt., 52(26), p. 6579. [CrossRef] [PubMed]
Schröder, S. , Herffurth, T. , Blaschke, H. , and Duparré, A. , 2011, “ Angle-Resolved Scattering: An Effective Method for Characterizing Thin-Film Coatings,” Appl. Opt., 50(9), p. C164. [CrossRef] [PubMed]
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VDA, 2010, Oberflächenbeschaffenheit: Geometrische Produktspezifikation; winkelaufgelöste Streulichtmesstechnik; Definition, Kenngrößen und Anwendung, 2010th ed., Verband der Automobilindustrie, Berlin.
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Figures

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Fig. 1

Virtual Zemax model of scattered light sensor and representation of coordinate systems to describe geometric correlations (Zemax model by Dipl.-Phys. Günter Beichert)

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Fig. 2

Scattering angle distribution

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Fig. 3

Visualization of intensity distribution across the diode array of the scattered light sensor when virtually measuring a super-fine level 1 Halle roughness standard (top image). Resulting virtual diode values shown in color (bottom image).

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Fig. 5

Different modeling approaches for convolution-based depiction of the transfer characteristic of the angle-resolved scattered light sensor when measuring rough surfaces. Collimated illumination of the surface (left illustration). Consideration of different angles of incidence depending on lateral position (right image).

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Fig. 4

Coherent intensity distribution on the rough surface of the topography as the result of a nonsequential ray-tracing simulation with 1,000,000 rays in Zemax (left image). Incoherent intensity distribution of the same Zemax simulation (right illustration).

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Fig. 9

Change in the Aq value after tilting a reflecting surface orthogonally to the diode array with: calculation by convolution with a homogeneous intensity distribution following modeling approach 1 (green), calculation with the ray-tracing program Zemax (red), mathematical calculation with an intensity distribution calculated using Zemax (modeling approach 1) (violet), and actual measurement (blue)

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Fig. 6

Incoherent intensity distribution on the virtual sensor as the result of reflection of illumination of the measuring spot simulated with Zemax (left illustration). Lateral shift by θx=2.5 deg and θy=5.0 deg of incoherent intensity distribution with inclination of a perfectly reflecting virtual mirror (right image).

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Fig. 7

Visualization of intensity distribution across the diode array of the scattered light sensor when measuring a virtual, perfectly aligned smoothness standard with the ray-tracing program Zemax (top image). Corresponding diode values are shown in color (bottom image).

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Fig. 8

Normalized intensity distribution of diode values with virtual scattered light measurement of a smoothness standard when intensity distribution is: calculated by convolution with a homogeneous intensity distribution (blue), calculated with the ray-tracing program Zemax (gray), and actually measured (red)

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Fig. 14

Course of the Aq value depending on the sphere radii measured virtually with the ray-tracing model of the scattered light sensor in Zemax and representation of the weighting-based smoothing function for approximating the Aq course

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Fig. 11

Geometric correlations when examining the gradient distribution on the surface of a sphere

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Fig. 12

Homogeneous intensity distribution with virtual scattered light measurement of sphere surfaces, measured on a virtual detector with 32 × 32 diodes for the radii RSphere=5 mm, RSphere=10 mm, and RSphere=15 mm

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Fig. 13

Aq course depending on the radius of a sphere in the lens focal point: actual measurement, simulation with the ray-tracing program Zemax (red) and calculation of convolution with a homogeneous intensity distribution (blue); one simulated with Zemax following modeling approach 1 (orange) and calculation of convolution with a homogeneous (green) intensity distribution; and one simulated with Zemax following model approach 2 (violet), as well as representation of the amount of deviation of the respective curves from the virtual reference

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Fig. 10

Incoherent intensity distribution as the result of virtual scattered light measurement on anisotropic, rough surfaces based on the optical transfer function of the virtual sensor model (modeling approach 1). Virtual measurement of the super-fine level 1 roughness standard (left illustration). Virtual measurement of the super-fine level 2 roughness standard (center illustration). Virtual measurement of the super-fine level 3 roughness standard (right illustration).

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Fig. 15

Aq course depending on the radius of a cylinder in the lens focal point: actual measurement of respective waves, simulation with the ray-tracing program Zemax (red), calculation of convolution with a homogeneous intensity distribution (blue); one simulated with Zemax following modeling approach 1 (orange) and calculation of convolution with a homogeneous (green) intensity distribution; and one simulated with Zemax following model approach 2 (violet), as well as representation of the amount of deviation of the respective curves from the virtual reference

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