Abstract

A multi-wavelength expansion of the Gerchberg-Saxton (GS) algorithm is developed to design and optimize a surface relief Diffractive Optical Element (DOE). The DOE simultaneously diffracts distinct wavelength bands into separate target regions. A description of the algorithm is provided, and parameters that affect filter performance are examined. Performance is based on the spectral power collected within specified regions on a receiver plane. The modified GS algorithm is used to design spectrum splitting optics for CdSe and Si photovoltaic (PV) cells. The DOE has average optical efficiency of 87.5% over the spectral bands of interest (400-710 nm and 710-1100 nm). Simulated PV conversion efficiency is 37.7%, which is 29.3% higher than the efficiency of the better performing PV cell without spectrum splitting optics.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Design of array of diffractive optical elements with inter-element coherent fan-outs

Johan Stigwall and Jörgen Bengtsson
Opt. Express 12(23) 5675-5683 (2004)

References

  • View by:
  • |
  • |
  • |

  1. O. Bryngdahl, “Geometrical transformations in optics,” J. Opt. Soc. Am. 64(8), 1092–1099 (1974).
    [Crossref]
  2. M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26(14), 2788–2798 (1987).
    [Crossref] [PubMed]
  3. Y. Lin, T. J. Kessler, and G. N. Lawrence, “Design of continuous surface-relief phase plates by surface-based simulated annealing to achieve control of focal-plane irradiance,” Opt. Lett. 21(20), 1703–1705 (1996).
    [Crossref] [PubMed]
  4. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3(1), 27–29 (1978).
    [Crossref] [PubMed]
  5. R. W. Gerchburg and W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).
  6. G. Z. Yang, B. Z. Dong, B. Y. Gu, J. Y. Zhuang, and O. K. Ersoy, “Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: a comparison,” Appl. Opt. 33(2), 209–218 (1994).
    [Crossref] [PubMed]
  7. E. G. Johnson and M. A. Abushagur, “Microgenetic-algoithm optimization methods applied to dielectric gratings,” J. Opt. Soc. Am. A 12(5), 1152–1160 (1995).
    [Crossref]
  8. P. Birch, R. Young, M. Farsari, C. Chatwin, and D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33(6), 439–448 (2000).
    [Crossref]
  9. G. Zhou, X. Yuan, P. Dowd, Y. L. Lam, and Y. C. Chan, “Design of diffractive phase elements for beam shaping: hybrid approach,” J. Opt. Soc. Am. A 18(4), 791–800 (2001).
    [Crossref]
  10. G. Zhou, Y. Chen, Z. Wang, and H. Song, “Genetic local search algorithm for optimization design of diffractive optical elements,” Appl. Opt. 38(20), 4281–4290 (1999).
    [Crossref] [PubMed]
  11. H. Kim, B. Yang, and B. Lee, “Iterative Fourier transform algorithm with regularization for the optimal design of diffractive optical elements,” J. Opt. Soc. Am. A 21(12), 2353–2365 (2004).
    [Crossref] [PubMed]
  12. B. Y. Gu, G. Z. Yang, B. Z. Dong, M. P. Chang, and O. K. Ersoy, “Diffractive-phase-element design that implements several optical functions,” Appl. Opt. 34(14), 2564–2570 (1995).
    [Crossref] [PubMed]
  13. B. Z. Dong, G. Q. Zhang, G. Z. Yang, B. Y. Gu, S. H. Zheng, D. H. Li, Y. S. Chen, X. M. Cui, M. L. Chen, and H. D. Liu, “Design and fabrication of a diffractive phase element for wavelength demultiplexing and spatial focusing simultaneously,” Appl. Opt. 35(35), 6859–6864 (1996).
    [Crossref] [PubMed]
  14. Y. Ogura, N. Shirai, J. Tanida, and Y. Ichioka, “Wavelength-multiplexing diffractive phase elements: design, fabrication, and performance evaluation,” J. Opt. Soc. Am. A 18(5), 1082–1092 (2001).
    [Crossref] [PubMed]
  15. T. R. Sales and D. H. Raguin, “Multiwavelength operation with thin diffractive elements,” Appl. Opt. 38(14), 3012–3018 (1999).
    [Crossref] [PubMed]
  16. J. Z. Wang, J. S. Ye, Q. L. Huang, X. Xu, D. M. Li, Q. B. Meng, and G. Z. Yang, “Design optimization of highly efficient spectrum-splitting and beam-concentrating diffractive optical element for lateral multijunction solar cells,” Chin. Phys. B 23(4), 044211 (2014).
    [Crossref]
  17. Q. Huang, J. Wang, B. Quan, Q. Zhang, D. Zhang, D. Li, Q. Meng, L. Pan, Y. Wang, and G. Yang, “Design and fabrication of a diffractive optical element as a spectrum-splitting solar concentrator for lateral multijunction solar cells,” Appl. Opt. 52(11), 2312–2319 (2013).
    [Crossref] [PubMed]
  18. G. Kim, J. A. Domínguez-Caballero, and R. Menon, “Design and analysis of multi-wavelength diffractive optics,” Opt. Express 20(3), 2814–2823 (2012).
    [Crossref] [PubMed]
  19. G. Kim, J. A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
    [Crossref] [PubMed]
  20. N. Mohammad, P. Wang, D. J. Friedman, and R. Menon, “Enhancing photovoltaic output power by 3-band spectrum-splitting and concentration using a diffractive micro-optic,” Opt. Express 22(106), A1519–A1525 (2014).
    [Crossref] [PubMed]
  21. J. A. Domínguez-Caballero, “Optimization of the holographic process for imaging and lithography,” Ph.D. Thesis, Massachusetts Institute of Technology (2010).
  22. R. Menon, “Ultra-high efficiency multi-junction solar cells using polychromatic diffractive concentrators,” United States Patent 8669461 (March 11, 2014).
  23. C. H. Henry, “Limiting efficiencies of ideal single and multiple energy gap terrestrial solar cells,” J. Appl. Phys. 51(8), 4494–4500 (1980).
    [Crossref]

2014 (2)

J. Z. Wang, J. S. Ye, Q. L. Huang, X. Xu, D. M. Li, Q. B. Meng, and G. Z. Yang, “Design optimization of highly efficient spectrum-splitting and beam-concentrating diffractive optical element for lateral multijunction solar cells,” Chin. Phys. B 23(4), 044211 (2014).
[Crossref]

N. Mohammad, P. Wang, D. J. Friedman, and R. Menon, “Enhancing photovoltaic output power by 3-band spectrum-splitting and concentration using a diffractive micro-optic,” Opt. Express 22(106), A1519–A1525 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (1)

2004 (1)

2001 (2)

2000 (1)

P. Birch, R. Young, M. Farsari, C. Chatwin, and D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33(6), 439–448 (2000).
[Crossref]

1999 (2)

1996 (2)

1995 (2)

1994 (1)

1987 (1)

1980 (1)

C. H. Henry, “Limiting efficiencies of ideal single and multiple energy gap terrestrial solar cells,” J. Appl. Phys. 51(8), 4494–4500 (1980).
[Crossref]

1978 (1)

1974 (1)

1972 (1)

R. W. Gerchburg and W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Abushagur, M. A.

Allebach, J. P.

Birch, P.

P. Birch, R. Young, M. Farsari, C. Chatwin, and D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33(6), 439–448 (2000).
[Crossref]

Bryngdahl, O.

Budgett, D.

P. Birch, R. Young, M. Farsari, C. Chatwin, and D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33(6), 439–448 (2000).
[Crossref]

Chan, Y. C.

Chang, M. P.

Chatwin, C.

P. Birch, R. Young, M. Farsari, C. Chatwin, and D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33(6), 439–448 (2000).
[Crossref]

Chen, M. L.

Chen, Y.

Chen, Y. S.

Cui, X. M.

Dominguez-Caballero, J. A.

G. Kim, J. A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[Crossref] [PubMed]

Domínguez-Caballero, J. A.

Dong, B. Z.

Dowd, P.

Ersoy, O. K.

Farsari, M.

P. Birch, R. Young, M. Farsari, C. Chatwin, and D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33(6), 439–448 (2000).
[Crossref]

Fienup, J. R.

Friedman, D. J.

N. Mohammad, P. Wang, D. J. Friedman, and R. Menon, “Enhancing photovoltaic output power by 3-band spectrum-splitting and concentration using a diffractive micro-optic,” Opt. Express 22(106), A1519–A1525 (2014).
[Crossref] [PubMed]

G. Kim, J. A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[Crossref] [PubMed]

Gerchburg, R. W.

R. W. Gerchburg and W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Gu, B. Y.

Henry, C. H.

C. H. Henry, “Limiting efficiencies of ideal single and multiple energy gap terrestrial solar cells,” J. Appl. Phys. 51(8), 4494–4500 (1980).
[Crossref]

Huang, Q.

Huang, Q. L.

J. Z. Wang, J. S. Ye, Q. L. Huang, X. Xu, D. M. Li, Q. B. Meng, and G. Z. Yang, “Design optimization of highly efficient spectrum-splitting and beam-concentrating diffractive optical element for lateral multijunction solar cells,” Chin. Phys. B 23(4), 044211 (2014).
[Crossref]

Ichioka, Y.

Johnson, E. G.

Kessler, T. J.

Kim, G.

G. Kim, J. A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[Crossref] [PubMed]

G. Kim, J. A. Domínguez-Caballero, and R. Menon, “Design and analysis of multi-wavelength diffractive optics,” Opt. Express 20(3), 2814–2823 (2012).
[Crossref] [PubMed]

Kim, H.

Lam, Y. L.

Lawrence, G. N.

Lee, B.

Lee, H.

G. Kim, J. A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[Crossref] [PubMed]

Li, D.

Li, D. H.

Li, D. M.

J. Z. Wang, J. S. Ye, Q. L. Huang, X. Xu, D. M. Li, Q. B. Meng, and G. Z. Yang, “Design optimization of highly efficient spectrum-splitting and beam-concentrating diffractive optical element for lateral multijunction solar cells,” Chin. Phys. B 23(4), 044211 (2014).
[Crossref]

Lin, Y.

Liu, H. D.

Meng, Q.

Meng, Q. B.

J. Z. Wang, J. S. Ye, Q. L. Huang, X. Xu, D. M. Li, Q. B. Meng, and G. Z. Yang, “Design optimization of highly efficient spectrum-splitting and beam-concentrating diffractive optical element for lateral multijunction solar cells,” Chin. Phys. B 23(4), 044211 (2014).
[Crossref]

Menon, R.

Mohammad, N.

Ogura, Y.

Pan, L.

Quan, B.

Raguin, D. H.

Sales, T. R.

Saxton, W. O.

R. W. Gerchburg and W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Seldowitz, M. A.

Shirai, N.

Song, H.

Sweeney, D. W.

Tanida, J.

Wang, J.

Wang, J. Z.

J. Z. Wang, J. S. Ye, Q. L. Huang, X. Xu, D. M. Li, Q. B. Meng, and G. Z. Yang, “Design optimization of highly efficient spectrum-splitting and beam-concentrating diffractive optical element for lateral multijunction solar cells,” Chin. Phys. B 23(4), 044211 (2014).
[Crossref]

Wang, P.

Wang, Y.

Wang, Z.

Xu, X.

J. Z. Wang, J. S. Ye, Q. L. Huang, X. Xu, D. M. Li, Q. B. Meng, and G. Z. Yang, “Design optimization of highly efficient spectrum-splitting and beam-concentrating diffractive optical element for lateral multijunction solar cells,” Chin. Phys. B 23(4), 044211 (2014).
[Crossref]

Yang, B.

Yang, G.

Yang, G. Z.

Ye, J. S.

J. Z. Wang, J. S. Ye, Q. L. Huang, X. Xu, D. M. Li, Q. B. Meng, and G. Z. Yang, “Design optimization of highly efficient spectrum-splitting and beam-concentrating diffractive optical element for lateral multijunction solar cells,” Chin. Phys. B 23(4), 044211 (2014).
[Crossref]

Young, R.

P. Birch, R. Young, M. Farsari, C. Chatwin, and D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33(6), 439–448 (2000).
[Crossref]

Yuan, X.

Zhang, D.

Zhang, G. Q.

Zhang, Q.

Zheng, S. H.

Zhou, G.

Zhuang, J. Y.

Appl. Opt. (7)

M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. 26(14), 2788–2798 (1987).
[Crossref] [PubMed]

G. Z. Yang, B. Z. Dong, B. Y. Gu, J. Y. Zhuang, and O. K. Ersoy, “Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: a comparison,” Appl. Opt. 33(2), 209–218 (1994).
[Crossref] [PubMed]

G. Zhou, Y. Chen, Z. Wang, and H. Song, “Genetic local search algorithm for optimization design of diffractive optical elements,” Appl. Opt. 38(20), 4281–4290 (1999).
[Crossref] [PubMed]

B. Y. Gu, G. Z. Yang, B. Z. Dong, M. P. Chang, and O. K. Ersoy, “Diffractive-phase-element design that implements several optical functions,” Appl. Opt. 34(14), 2564–2570 (1995).
[Crossref] [PubMed]

B. Z. Dong, G. Q. Zhang, G. Z. Yang, B. Y. Gu, S. H. Zheng, D. H. Li, Y. S. Chen, X. M. Cui, M. L. Chen, and H. D. Liu, “Design and fabrication of a diffractive phase element for wavelength demultiplexing and spatial focusing simultaneously,” Appl. Opt. 35(35), 6859–6864 (1996).
[Crossref] [PubMed]

T. R. Sales and D. H. Raguin, “Multiwavelength operation with thin diffractive elements,” Appl. Opt. 38(14), 3012–3018 (1999).
[Crossref] [PubMed]

Q. Huang, J. Wang, B. Quan, Q. Zhang, D. Zhang, D. Li, Q. Meng, L. Pan, Y. Wang, and G. Yang, “Design and fabrication of a diffractive optical element as a spectrum-splitting solar concentrator for lateral multijunction solar cells,” Appl. Opt. 52(11), 2312–2319 (2013).
[Crossref] [PubMed]

Chin. Phys. B (1)

J. Z. Wang, J. S. Ye, Q. L. Huang, X. Xu, D. M. Li, Q. B. Meng, and G. Z. Yang, “Design optimization of highly efficient spectrum-splitting and beam-concentrating diffractive optical element for lateral multijunction solar cells,” Chin. Phys. B 23(4), 044211 (2014).
[Crossref]

J. Appl. Phys. (1)

C. H. Henry, “Limiting efficiencies of ideal single and multiple energy gap terrestrial solar cells,” J. Appl. Phys. 51(8), 4494–4500 (1980).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Opt. Express (2)

Opt. Lasers Eng. (1)

P. Birch, R. Young, M. Farsari, C. Chatwin, and D. Budgett, “A comparison of the iterative Fourier transform method and evolutionary algorithms for the design of diffractive optical elements,” Opt. Lasers Eng. 33(6), 439–448 (2000).
[Crossref]

Opt. Lett. (2)

Optik (Stuttg.) (1)

R. W. Gerchburg and W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Phys. Rev. Lett. (1)

G. Kim, J. A. Dominguez-Caballero, H. Lee, D. J. Friedman, and R. Menon, “Increased photovoltaic power output via diffractive spectrum separation,” Phys. Rev. Lett. 110(12), 123901 (2013).
[Crossref] [PubMed]

Other (2)

J. A. Domínguez-Caballero, “Optimization of the holographic process for imaging and lithography,” Ph.D. Thesis, Massachusetts Institute of Technology (2010).

R. Menon, “Ultra-high efficiency multi-junction solar cells using polychromatic diffractive concentrators,” United States Patent 8669461 (March 11, 2014).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (19)

Fig. 1
Fig. 1 System layout. Multiple wavelengths (λi) are incident on the DOE and diffract from the DOE plane to the diffracted plane located at distance zd.
Fig. 2
Fig. 2 Set of potential height levels for a DOE pixel with 4 design wavelengths and maximum height of 6µm. The set of heights with minimum range is circled. Final pixel height is a weighted average of these values.
Fig. 3
Fig. 3 Block diagram of broadband Gerchberg-Saxton algorithm.
Fig. 4
Fig. 4 Progression of SNR metric for two optimization runs. a. Stable SNR for a system with a 1 design wavelength assigned to each target region. b. Unstable SNR for a system which is overly-constrained with 2 design wavelengths assigned to each target region (0.4 and 0.6 μm; 0.8 and 1.0 μm).
Fig. 5
Fig. 5 Schematic of spectrum splitting module. The unit cell contains a DOE of width w, and an arrangement of PV cells at the diffracted distance zd. Two equal-area PV cells fill the plane, and the larger bandgap cell is placed in the center. The device repeats in the lateral direction and extends out-of-plane.
Fig. 6
Fig. 6 Spectral optical efficiency for baseline DOE
Fig. 7
Fig. 7 Height profile of baseline DOE
Fig. 8
Fig. 8 Spectral optical efficiency for a. decreased pixel width, b. increased pixel width.
Fig. 9
Fig. 9 Spectral optical efficiency for a. decreased diffracted distance, b. increased diffracted distance.
Fig. 10
Fig. 10 Spectral optical efficiency for a. decreased maximum DOE height, b. increased maximum DOE height.
Fig. 11
Fig. 11 Spectral distribution of irradiance along diffracted plane for DOEs with maximum height of a. 2.5 μm and b. 9μm.
Fig. 12
Fig. 12 Spectral optical efficiency for a. decreased difference in design wavelengths, b. increased difference in design wavelengths.
Fig. 13
Fig. 13 Spectral distribution of irradiance along diffracted plane for DOE with a small difference in design wavelengths (0.69 μm and 0.71 μm).
Fig. 14
Fig. 14 Spectral optical efficiency for a. W = [0.95 0.05], b. W = [0.05 0.95].
Fig. 15
Fig. 15 Spectral optical efficiency for an increased number of design wavelengths [0.4 0.6 0.8 1.0] μm and W = [0.325 0.325 0.175 0.175].
Fig. 16
Fig. 16 Spectral optical efficiency for a. a material with a greater degree of normal dispersion, and b. a material with anomalous dispersion.
Fig. 17
Fig. 17 Parameter scan of OAvg vs. a. pixel width, b. diffracted distance, c. maximum DOE height, d. difference in design wavelengths, e. weight factor.
Fig. 18
Fig. 18 Spectral optical efficiency for a. baseline simulation, b. best-case simulation.
Fig. 19
Fig. 19 Spectral optical efficiency for a range of incident angles for DOE with a diffracted distance of 2 cm.

Tables (2)

Tables Icon

Table 1 Starting Parameters for a CdSe/Si Spectrum Splitting DOE Design

Tables Icon

Table 2 Parameters for Best-Case DOE Simulation

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

u 1 ( x 1 ) = a 1 ( x 1 ) e i ϕ 1 ( x 1 )
u 2 ( x 2 ) = a 2 ( x 2 ) e i ϕ 2 ( x 2 )
u 1 j , i n i t i a l ( x 1 , λ j ) = exp ( i π x 1 2 λ j z d ) I F T [ i λ j z d Δ x exp ( i 2 π z d λ j ) exp ( i π x 2 2 λ j z d ) u 2 j ( x 2 , λ j ) ]
h j ( x 1 , λ j ) = λ j ϕ 1 j , i n i t i a l ( x 1 , λ j ) 2 π ( n ( λ j ) 1 )
h j k ( x 1 , λ j , k ) = λ j ( ϕ 1 j , i n i t i a l ( x 1 , λ j ) + 2 π k ) 2 π ( n ( λ j ) 1 ) k = 1 , 2 , ... k max
h ( x 1 ) = j w j h j
ϕ 1 j ( x 1 , λ j ) = 2 π h ( x 1 ) λ j ( n ( λ j ) 1 )
u 1 j ( x 1 , λ j ) = exp ( i ϕ 1 j ( x 1 , λ j ) )
u 2 j , i n i t i a l ( x 2 , λ j ) = i Δ x λ j z d exp ( i 2 π z d λ j ) exp ( i π x 2 2 λ j z d ) F T [ exp ( i π x 1 2 λ j z d ) u 2 j ( x 2 , λ j ) Δ x ]
u 2 j ( x 2 , λ j ) = { 0 a 2 j ( x 2 , λ j ) exp ( i ϕ 2 j ( x 2 , λ j ) ) x 2 outside of target region x 2 within target region
S N R = λ j x 2 Target I 2 j ( x 2 , λ j ) d x 2 x 2 Non-Target I 2 j ( x 2 , λ j ) d x 2
S O E ( λ ) = x 2 Target I 2 ( x 2 , λ ) d x 2 x 1 I 1 ( x 1 , λ ) d x 1 100
O A v g = λ 1 λ 2 S O E ( λ ) d λ 100 ( λ 2 λ 1 ) 100
I o B B = ( η S S η B e s t P V 1 ) 100
| θ min | = sin 1 ( λ min 2 Δ x )
d min = w 4 tan [ sin 1 ( λ min 2 Δ x ) ]
z l = z d f z d + f
O P D = h ( n ( λ ) 1 )
1 λ P = h ( n ( λ P ) 1 )
2 λ S = h ( n ( λ S ) 1 )
λ S = ( λ P 2 ) ( n ( λ S ) 1 n ( λ P ) 1 )
n ( λ P ) = n ( λ S ) λ S = λ P 2
n ( λ P ) < n ( λ S ) λ S > λ P 2
n ( λ P ) > n ( λ S ) λ S < λ P 2

Metrics