Abstract

It is difficult to solve the problem of tracing rays through an inhomogeneous medium such as the atmosphere or a flowing liquid with the existing methods whose refractive distribution cannot be characterized by any combination of formulas. A new method is developed to efficiently describe such a medium. The method essentially consists of characterizing the inhomogeneous medium with a self-adapting grid, the cell size of which can be automatically varied according to the gradient of the refractive index at each position within the medium. The advantage of this method is its capability to trace rays through a medium with random refractive distribution in an accurate way. To test its correctness, the ray trace through a regular gradient medium has also been made with this method, and the results are compared with those from other commercial lens design codes. It is shown that for appropriate parameter settings this method can obtain great accuracy.

© 2007 Optical Society of America

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References

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  1. X. H. Sun, H. Ma, H. Ming, Z. Q. Zheng, J. W. Yang, and J. P. Xie, "The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method," Opt. Laser Technol. 36, 163-166 (2004).
    [CrossRef]
  2. P. Ben Abdallah and V. Le Dez, "Thermal emission of a semitransparent slab with variable spatial refractive index," J. Quant. Spectrosc. Radiat. Transfer 67, 185-198 (2000).
    [CrossRef]
  3. E. W. Marchand, Gradient Index Optics (Academic, 1978).
  4. L. H. Liu, K. Kudo, and B. X. Li, "Comparison of ray-tracing methods for semitransparent slab with variable spatial refractive index," J. Quant. Spectrosc. Radiat. Transfer 85, 125-133 (2004).
    [CrossRef]
  5. A. Sharma, D. V. Kumar, and A. K. Ghatak, "Tracing rays through graded-index media: a new method," Appl. Opt. 21, 984-987 (1982).
    [CrossRef] [PubMed]
  6. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

2004

X. H. Sun, H. Ma, H. Ming, Z. Q. Zheng, J. W. Yang, and J. P. Xie, "The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method," Opt. Laser Technol. 36, 163-166 (2004).
[CrossRef]

L. H. Liu, K. Kudo, and B. X. Li, "Comparison of ray-tracing methods for semitransparent slab with variable spatial refractive index," J. Quant. Spectrosc. Radiat. Transfer 85, 125-133 (2004).
[CrossRef]

2000

P. Ben Abdallah and V. Le Dez, "Thermal emission of a semitransparent slab with variable spatial refractive index," J. Quant. Spectrosc. Radiat. Transfer 67, 185-198 (2000).
[CrossRef]

1982

Abdallah, P. Ben

P. Ben Abdallah and V. Le Dez, "Thermal emission of a semitransparent slab with variable spatial refractive index," J. Quant. Spectrosc. Radiat. Transfer 67, 185-198 (2000).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Ghatak, A. K.

Kudo, K.

L. H. Liu, K. Kudo, and B. X. Li, "Comparison of ray-tracing methods for semitransparent slab with variable spatial refractive index," J. Quant. Spectrosc. Radiat. Transfer 85, 125-133 (2004).
[CrossRef]

Kumar, D. V.

Le Dez, V.

P. Ben Abdallah and V. Le Dez, "Thermal emission of a semitransparent slab with variable spatial refractive index," J. Quant. Spectrosc. Radiat. Transfer 67, 185-198 (2000).
[CrossRef]

Li, B. X.

L. H. Liu, K. Kudo, and B. X. Li, "Comparison of ray-tracing methods for semitransparent slab with variable spatial refractive index," J. Quant. Spectrosc. Radiat. Transfer 85, 125-133 (2004).
[CrossRef]

Liu, L. H.

L. H. Liu, K. Kudo, and B. X. Li, "Comparison of ray-tracing methods for semitransparent slab with variable spatial refractive index," J. Quant. Spectrosc. Radiat. Transfer 85, 125-133 (2004).
[CrossRef]

Ma, H.

X. H. Sun, H. Ma, H. Ming, Z. Q. Zheng, J. W. Yang, and J. P. Xie, "The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method," Opt. Laser Technol. 36, 163-166 (2004).
[CrossRef]

Marchand, E. W.

E. W. Marchand, Gradient Index Optics (Academic, 1978).

Ming, H.

X. H. Sun, H. Ma, H. Ming, Z. Q. Zheng, J. W. Yang, and J. P. Xie, "The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method," Opt. Laser Technol. 36, 163-166 (2004).
[CrossRef]

Sharma, A.

Sun, X. H.

X. H. Sun, H. Ma, H. Ming, Z. Q. Zheng, J. W. Yang, and J. P. Xie, "The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method," Opt. Laser Technol. 36, 163-166 (2004).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Xie, J. P.

X. H. Sun, H. Ma, H. Ming, Z. Q. Zheng, J. W. Yang, and J. P. Xie, "The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method," Opt. Laser Technol. 36, 163-166 (2004).
[CrossRef]

Yang, J. W.

X. H. Sun, H. Ma, H. Ming, Z. Q. Zheng, J. W. Yang, and J. P. Xie, "The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method," Opt. Laser Technol. 36, 163-166 (2004).
[CrossRef]

Zheng, Z. Q.

X. H. Sun, H. Ma, H. Ming, Z. Q. Zheng, J. W. Yang, and J. P. Xie, "The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method," Opt. Laser Technol. 36, 163-166 (2004).
[CrossRef]

Appl. Opt.

J. Quant. Spectrosc. Radiat. Transfer

P. Ben Abdallah and V. Le Dez, "Thermal emission of a semitransparent slab with variable spatial refractive index," J. Quant. Spectrosc. Radiat. Transfer 67, 185-198 (2000).
[CrossRef]

L. H. Liu, K. Kudo, and B. X. Li, "Comparison of ray-tracing methods for semitransparent slab with variable spatial refractive index," J. Quant. Spectrosc. Radiat. Transfer 85, 125-133 (2004).
[CrossRef]

Opt. Laser Technol.

X. H. Sun, H. Ma, H. Ming, Z. Q. Zheng, J. W. Yang, and J. P. Xie, "The measurement of refractive index profile and aberration of radial gradient index lens by using imaging method," Opt. Laser Technol. 36, 163-166 (2004).
[CrossRef]

Other

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

E. W. Marchand, Gradient Index Optics (Academic, 1978).

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Figures (7)

Fig. 1
Fig. 1

Schematic of the liquid flow field.

Fig. 2
Fig. 2

Cross-sectional view of the self-adapting grid.

Fig. 3
Fig. 3

Octa tree data structure for storing the refractive index value.

Fig. 4
Fig. 4

Ray trace in the graded-index medium.

Fig. 5
Fig. 5

Comparison of 2D layout for a ray trace with a self-adapting grid and Zemax.

Fig. 6
Fig. 6

(Color online) Color-scale map of the refractive distribution in a liquid flow field.

Fig. 7
Fig. 7

Wavefront map of the exit pupil by ray trace through a random index medium.

Tables (2)

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Table 1 Excerpt of the Provided Refractive Index Distribution Data

Tables Icon

Table 2 RMS of the Spot Diagram Size by Different Interpolation Methods and Zemax

Equations (3)

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d d s [ n ( r ) d r d s ] = n ( r ) ,
n ( P ) = n ( B ) + grad Δ s ,
n = n 0 + n r 2 r 2 ,

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