7/24/2019 Survey on optical deflectometry to evaluate the topography of three-dimensional surfaces

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Surveyonopticaldeflectometrytoevaluate thetopographyofthree-dimensionalsurfaces

Rigoberto Juarez-Salazar1,, W. Fermin Guerrero Sanchez2, Carlos I. Robledo Sanchez2, CesarAlejandro Lopez Ortiz1, Jorge Gonzalez Garcia1 and Agustin Santiago Alvarado1

1Instituto de Fsica y Matemticas, Universidad Tecnolgica de la Mixteca2Facultad de Ciencias Fsico-Matemticas, Benemrita Universidad Autnoma de Puebla

rjuarezsalazar@gmail.com

bstractptical deflectometry hasa greatinterestin evaluation

surfaces because of its high sensitivity. In this work,e present a survey on optical deflectometry to evalu-e the topography of three-dimensional surfaces. Weow experimental results obtained from evaluationa surface for solar concentration.

troductionptical deflectometry methods are widely used be-use of its higher sensitivity, in some applications,ar to interferometric levels [1, 2]. However, unlikefringe projection techniques, the topography eval-tion is not direct with deflectometry [4]. Moreover,e measurement depends on the optical arrangement

mployed [3].

e present a survey of optical deflectometry to evalu-e the topography of 3D surfaces. The relevant itemsnbe classifiedinto twodifferent problems: thedirectd inverse problems. They were analyzed and somesults analyzing a mirror for solar concentration.

onclusionse data processing is hard and computer time. In thisrvey, the direct and inverse problems in deflectome-yapproachwherepresented. Fourmethods to recon-ucta concave spherical mirror where suggested. Weow the effectiveness of a proposed method in a nu-erical simulation and good results where obtained.

o you wish to learn more?et the full document, supplementary materials andated papers.

Direct reflection problemDeflectometry is based mainly in the Snells reflection

law. Two conditions must be satisfied:

1. The incident ray, the reflected ray and the nor-mal at the reflection points are coplanar, and

2. The angles formed by the normal-incident rayand normal-reflected ray are equals.

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The so-called ray tracing methods are based on theabove restrictions. This approach offers useful results

to design optical elements and/or to analyze the per-formance of experimental arrangements.

Solutions methods and resultsFor simplicity purposes, we consider a concave spherical surface and four inverse reflection methoposed.

1. By using the inner product and requiring the constraint rac= rbc, Fig. 1(a).

2. Finding the intersection pointc, then to apply the angle bisector theorem m/n= ||c a||/||c b

3. Computing the intersection pointsa and b, then the line between them and the radius are foorthogonal; i.e.,(a b)c= 0 , Fig. 1(c).

4. From the spherical coordinates of vectors caandcbto compute the angle which satisfies th= (a+b)/2, Fig. 1(d).

c

a

b

c

a

b

c'

m n

c

a

b

b'

b'

a'

a

c'

(a) (b) (c) (d)

Fig. 1. Four methods to solve the inverse reflection problem in a concave spherical mirror.

The last described method was used in the tree-dimensional reconstruction of a concave spherical show in Fig. 2 the procedure of reconstruction.

Fig. 2. Reconstruction of a concave spherical mirror by using the method in Fig. 1(d). (Left) Computiof from a point on the output image. (Right) All corresponding points sensed on the output im

Inverse reflection problemOn the other hand, the deflectometry me

can be see in one of the following situation

1. From the known output and opticaldetermine the input object, and

2. From the known output and input objtermine the optical system.

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eferencesC. Faber, E. Olesch, R. Krobot, and G. Hdusler. Deflectometrychallenges interferometry: the competition gets tougher! Proc.SPIE, 8493:84930R84930R15, 2012.A. Miks, J. Novak, and P. Novak. Method for reconstruction ofshape of specular surfaces using scanning beam deflectometry.Optics and Lasers in Engineering, 51(7):867 872, 2013.J. Novak, P. Novak, and A. Miks. Analysis of method of 3dshape reconstruction using scanning deflectometry, 2013.G. Sironi, R. Canestrari, G. Pareschi, and C. Pelliciari. Deflec-tometry for opticsevaluation: freeform segments of polynomialmirror, 2014.