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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 17 — Aug. 15, 2011
  • pp: 15750–15759
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Achromatic design in the illumination system for a mini projector with LED light source

Jui-Wen Pan and Sheng-Han Lin  »View Author Affiliations


Optics Express, Vol. 19, Issue 17, pp. 15750-15759 (2011)
http://dx.doi.org/10.1364/OE.19.015750


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Abstract

We provide a novel achromatic design in the illumination system for a mini projector with an LED light source. The lateral color aberration at the corners of the DMD active area can be reduced to 0.48 μm by our compact ATIR prism. The total prism size is 4091 mm3. The spot sizes at the corner and the edge are also controlled under 198 μm. Moreover, we use a light pipe for color uniformity at the center of the DMD active area. Under the two components for color uniformity, the Δu’ v’ is well controlled under 0.016 by a 20 mm length of light pipe. The illuminance uniformity at the active area of the DMD chip is higher than 92.8%. The optical efficiency of the light pipe is 94.1%.

© 2011 OSA

1. Introduction

Light-emitting diodes (LEDs) are the new generation of light sources. LEDs are power-saving and environmentally friendly [1

1. E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science 308(5726), 1274–1278 (2005). [CrossRef] [PubMed]

]. A long life and a small size are also common properties of LEDs. With the development of this technology various LED applications have been developed, and it also has created amazing business opportunities. In addition to well-known electronic products such as the LED indicator and signal lantern, there are many LED application products such as the backlight in a liquid crystal display (LCD) for mobile phones and other products. In projector products, an LED light source has been widely used for digital light processing (DLP) and liquid crystal on silicon (LCoS) projectors [2

2. Texas Instruments (TI), “DLP® Discovery Optics 101 Application Note,” http://focus.ti.com/lit/an/dlpa022/dlpa022.pdf.

,3

3. H. Murat, D. Cuypers, H. De Smet, Y. Meuret, B. Van Giel, L. Bogaert, and H. Thienpont, “Two liquid crystal on silicon panel projector with efficient light-emitting diode illumination,” Opt. Eng. 46(12), 124002 (2007). [CrossRef]

].

In DLP projectors [4

4. C.-M. Chang and H.-P. D. Shieh, “Design of illumination and projection optics for projectors with single digital micromirror devices,” Appl. Opt. 39(19), 3202–3208 (2000). [CrossRef] [PubMed]

], there are many advantages in replacing a conventional ultra-high-pressure (UHP) lamp with an LED light source [5

5. J.-W. Pan, S.-H. Tu, C.-M. Wang, and J.-Y. Chang, “High efficiency pocket-size projector with a compact projection lens and a light emitting diode-based light source system,” Appl. Opt. 47(19), 3406–3414 (2008). [CrossRef] [PubMed]

8

8. M. H. Keuper, G. Harbers, and S. Paolini, “RGB LED Illuminator for Pocket-sized Projectors,” in International Symposium Digest of Technical Papers (SID ’04), 943–945 (2004).

]. Most of all, an LED light source has highly saturated color with a narrow bandwidth [9

9. M. Huseyin, C. Dieter, and D. S. Herbert, “Design of new collection systems for multi LED light engines,” Proc. SPIE 6196, 19604 (2006).

]. However, the red, green, and blue (RGB) LEDs are separate light sources in a DLP projector. According to our research, “Homogenized LED-illumination using microlens arrays for a pocket-sized projector [10

10. J. W. Pan, C. M. Wang, H. C. Lan, W. S. Sun, and J. Y. Chang, “Homogenized LED-illumination using microlens arrays for a pocket-sized projector,” Opt. Express 15(17), 10483–10491 (2007). [CrossRef] [PubMed]

],” we used an LED light source in our mini projector where there are serious color uniformity issues at the center and corner of the projection screen.

In this paper, we introduce novel achromatic prisms in the illumination system of a projector in order to solve the lateral color aberration at the corner of the digital micromirror device (DMD) active area and to control color uniformity at the center of the DMD active area with a light pipe. For lateral color aberration, a novel achromatic prism is designed to reduce lateral color aberration at the corner of the DMD active area to under 10 μm. We do not use any achromatic doublet lenses to reduce the lateral color aberration produced in the illumination system with a total internal reflection (TIR) prism [10

10. J. W. Pan, C. M. Wang, H. C. Lan, W. S. Sun, and J. Y. Chang, “Homogenized LED-illumination using microlens arrays for a pocket-sized projector,” Opt. Express 15(17), 10483–10491 (2007). [CrossRef] [PubMed]

]. We have a compact prism size of 4091 mm3. The spot sizes (SPT) at the corner and the edge of the DMD active area are also controlled under 198 μm. For color uniformity we use a light pipe to control the color uniformity at the center of the DMD active area. There is a trade-off between the length of the light pipe and its optical efficiency. The longer light pipe brings us better color uniformity with lower optical efficiency. Finally, the Δu’ v’ is also controlled under 0.016 with a 20 mm length of light pipe. In addition to color uniformity, illuminance uniformity is also investigated. We can use a light pipe to enhance illuminance uniformity from a highly peaked distribution to a relatively uniform and flat distribution at the exit point of the light pipe. Moreover, we can also get illuminance uniformity at the DMD active area by choosing a suitable length of a hollow-mirrored light pipe with low-loss efficiency [11

11. E. H. Stupp and M. S. Brennesholtz, Projection Display, (Wiley, 2008).

,12

12. J. W. Pan, C. M. Wang, W. S. Sun, and J. Y. Chang, “Portable digital micromirror device projector using a prism,” Appl. Opt. 46(22), 5097–5102 (2007). [CrossRef] [PubMed]

]. The illuminance uniformity at the DMD active area is higher than 92.8%.

2. The Achromatic TIR Prism for Lateral Color Aberration

We used two optical materials to make up the ATIR prism. A is the prism angle of the first prism, as shown in Fig. 1. Then na and nb are the indices at d light for the first and second prisms. θin and θDMD are the incident angles at the ATIR prism and the DMD active area. θDMD is 26.5 degrees for higher contrast and lower loss [12

12. J. W. Pan, C. M. Wang, W. S. Sun, and J. Y. Chang, “Portable digital micromirror device projector using a prism,” Appl. Opt. 46(22), 5097–5102 (2007). [CrossRef] [PubMed]

]. For an illumination system with an ATIR prism, the optical axis will pass through the ATIR prism and impinge on the DMD active area. θin, θDMD, and the index of two different materials for the optical axis will follow Eq. (1):

sinθin=nasin{sin1[nbnasin(45sin1sinθDMDnb)]A}.
(1)

Besides lateral color aberration, spot size on a DMD active area is a very important factor for an illumination system. We also discuss the relation between spot size, prism size, and incident angle for the four real optical materials, as shown in Fig. 3
Fig. 3 Spot size on the DMD active area and the prism size for a series of incident angle (θin). (a) Spot size of SK16. (b) Spot size of SF2. (c) Spot size of LAK8. (d) Spot size of SF57.
. We evaluate the spot size on the DMD active area by the rms value. The spot sizes located at the center, corner, and edge of the DMD active area are: a green triangle, a red square, and a blue counter triangle. The spot size increases when the incident angle increases. As we mentioned before, in Fig. 3 the prism size decreases when the incident angle increases. In other words, the spot size increases when the prism size decreases. In Fig. 3, for an incident angle around 7 to 10 degrees, the average spot size for the center, corner, and edge is at the lowest level and the minimum spot size is controlled under 100 μm.

In addition, we must consider the cost issue for an ATIR prism. An expensive material is not practical for a manufacturer. In order to get the lowest lateral color aberration for the color uniformity issue at the corner of a DMD active area, we summarize all of the optical properties for the four used materials in Table 1

Table 1. Comparison for Novel ATIR Prism with Different Material

table-icon
View This Table
. For each achromatic material, Table 1 shows spot size, prism size, and glass price. The Schott glass price data in Table 1 refers to Ohara’s reference sheet with the corresponding glass catalog [15

15. Ohara Corporation, “Optical Glass Cross Reference Sheet, http://www.oharacorp.com/catalog.html.

]. Overall in Table 1, N-SF2 is the optical material with the best balance between low lateral color aberration, small spot size, compact prism size, and low cost. For lateral color aberration and compact prism size, we can choose N-SF57 for the first prism with a high incident angle, but the price for N-SF57 is too expensive. Moreover, the spot size is largest at the corner of the DMD chip. For the lateral color aberration, small spot size and cost issue, we can choose N-SK16 for the first prism with a low incident angle. However, the prism size of N-SK16 is the largest. The lateral color aberration of N-SK16 is the highest, because the Abbe number of N-SK16 is too close to the Abbe number of N-BK7. In this paper, N-SF2 is our final choice for the ATIR prism.

3. Light Pipe for Color Uniformity

The light pipe is formed by four silver mirrors with a cross section of 5.0 × 3.8 mm. The magnification between the exit of the light pipe and the DMD active area is 2.4 × with a 10% over-fill loss for mass production [11

11. E. H. Stupp and M. S. Brennesholtz, Projection Display, (Wiley, 2008).

]. The typical reflectivity for four silver mirrors is 98%. The length of the light pipe is relative to the uniformity degree at the DMD active area. In order to find a suitable length of light pipe, we must define some parameters to evaluate optical performance. First, we define over-filled efficiency as the ratio of the flux in the DMD active area and the flux in the entire DMD chip [10

10. J. W. Pan, C. M. Wang, H. C. Lan, W. S. Sun, and J. Y. Chang, “Homogenized LED-illumination using microlens arrays for a pocket-sized projector,” Opt. Express 15(17), 10483–10491 (2007). [CrossRef] [PubMed]

]. The mathematical equation is shown in Eq. (2), where Factive is the flux at the DMD active area, and FDMD is the total flux of the entire DMD chip. Second, color uniformity is one of our main issues in an achromatic design. Color uniformity is relative to Δu’ v’, so we chose nine points on the receiver and use the average value of Δu’ v’ to represent color uniformity. Δu’ v’ is defined by Eq. (3) [16

16. G. W. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative data and Formulae, (John Wiley & Sons, 1982).

]; u’ and v’ are the color coordinates for the current output color; and u’ref and v’ref are the color coordinates for the reference color. We use Osram Ostar SMT LEA_S2W, LET_S2W, and LEB_S2W LEDs as our light sources [17]. RGB LEDs are driven under a duty cycle of Red = 32.0%, Green = 37.6%, and Blue = 30.4% [16

16. G. W. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative data and Formulae, (John Wiley & Sons, 1982).

]. The reference chromaticity coordinate is (u’, v’) = (0.190, 0.450), which represents a color temperature of 8500K [11

11. E. H. Stupp and M. S. Brennesholtz, Projection Display, (Wiley, 2008).

,16

16. G. W. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative data and Formulae, (John Wiley & Sons, 1982).

]. In addition to color uniformity, we also investigate illuminance uniformity. We can use a light pipe to redistribute illuminance uniformity from a highly peaked distribution to a relatively uniform and flat distribution at the exit of the light pipe. We can get illuminance uniformity by choosing a suitable length of a hollow-mirrored light pipe with low-loss efficiency [11

11. E. H. Stupp and M. S. Brennesholtz, Projection Display, (Wiley, 2008).

,12

12. J. W. Pan, C. M. Wang, W. S. Sun, and J. Y. Chang, “Portable digital micromirror device projector using a prism,” Appl. Opt. 46(22), 5097–5102 (2007). [CrossRef] [PubMed]

]. Illuminance uniformity at the DMD active area is defined by Eq. (4). Li min is the minimum illuminance and Li max is the maximum illuminace in the illumination area. In addition, we must check the optical efficiency of the light pipe to maintain the optical efficiency of the light pipe. The optical efficiency of the light pipe is defined by Eq. (5), where Finput is the flux on the input of the light pipe and Foutput is the flux on the exit of the light pipe.

OverFilledEfficiency=FactiveFDMD×100%,
(2)
Average(Δuv)=i=19(uiuref)2+(vivref)29,
(3)
Illuminance  Uniformity=LminLmax×100%,
(4)
Optical  Efficiency of Light Pipe=FoutputFinput×100%.
(5)

For the optical simulations in this section, we used LightTools software [18] as our calculation platform. The relation between illuminance uniformity, the optical efficiency of a light pipe, and the length of the light pipe are shown in Fig. 4
Fig. 4 Efficiency and illuminance uniformity.
. The optical efficiency of a light pipe decreases linearly when the length of the light pipe increases, so we have to choose a suitable length of light pipe with low-loss efficiency [11

11. E. H. Stupp and M. S. Brennesholtz, Projection Display, (Wiley, 2008).

,12

12. J. W. Pan, C. M. Wang, W. S. Sun, and J. Y. Chang, “Portable digital micromirror device projector using a prism,” Appl. Opt. 46(22), 5097–5102 (2007). [CrossRef] [PubMed]

]. The illuminance uniformity increases when the length of the light pipe increases. Importantly, the illuminance uniformity at the DMD active area and the optical efficiency of a light pipe are higher than 90% when the light pipe is longer than 16 mm. Owing to this condition, we can choose a length of light pipe of 16 mm for illuminance uniformity. Figure 5
Fig. 5 Efficiency and average Δu’ v’.
shows the relation between Δu’ v’, the optical efficiency of the light pipe, and the length of the light pipe. The Δu’ v’ decreases when the length of the light pipe increases, which means the color uniformity increases when the length of the light pipe increases. In Fig. 5, the Δu’ v’ at the DMD active area with an ATIR prism stabilizes under 0.016 when the light pipe is longer than 20 mm. For color uniformity, we can choose a length of light pipe of 20 mm with 94.1% optical efficiency. Moreover, the difference between the Δu’ v’ at the DMD active area with the TIR prism [10

10. J. W. Pan, C. M. Wang, H. C. Lan, W. S. Sun, and J. Y. Chang, “Homogenized LED-illumination using microlens arrays for a pocket-sized projector,” Opt. Express 15(17), 10483–10491 (2007). [CrossRef] [PubMed]

] and the ATIR prism is shown in Fig. 5. The ATIR prism contributes to color uniformity and reduces Δu’ v’. At the DMD active area Δu’ v’ with the ATIR prism is 0.001 lower than Δu’ v’ with the TIR prism [10

10. J. W. Pan, C. M. Wang, H. C. Lan, W. S. Sun, and J. Y. Chang, “Homogenized LED-illumination using microlens arrays for a pocket-sized projector,” Opt. Express 15(17), 10483–10491 (2007). [CrossRef] [PubMed]

]. In Fig. 4 and Fig. 5, the optical efficiency of a light pipe decreases only 0.8% when the length of the light pipe is from 16 mm to 20 mm. We can control both the illuminance uniformity and the color uniformity well with an optical efficiency of light pipe higher than 90%.

4. Fabrication Tolerances of the LED Chip

Fabrication tolerance is an important consideration for a real optical manufacturer. RGB LEDs are installed in the light source respectively. In this case, there must be tolerances in fabrication. Tolerance for the linear dimension of an LED chip position is ± 0.25 mm [19

19. W. J. Smith, “Prism and Mirror Systems,” in Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008), pp. 619–621.

]. In this paper, we keep the illumination uniformity at the active area of a DMD chip higher than 90.0% and control the average Δu’ v’ at the DMD active area under 0.016, so we have to find tolerance under this condition. Human eyes are most sensitive to a green LED, so we fix the position of the green LED and shifted the positions of red and blue LEDs, respectively, in the linear dimension. Figure 8
Fig. 8 Tolerance for illumination uniformity.
shows the relation between illuminance uniformity and the displacement of the LEDs. The displacement of the LEDs can slightly influence illuminance uniformity at the DMD active area when we shift the positions of red and blue LEDs about 0.30 mm in the vertical and horizontal directions. Figure 9
Fig. 9 Tolerance for the average Δu’ v’.
shows the relation between the Δu’ v’ at the DMD active area and the displacement of the LEDs. When we shift the positions of red or blue LEDs from 0.05 mm to 0.30 mm, the average Δu’ v’ at the DMD active area is well controlled under 0.016.

5. Conclusion

In this paper, we demonstrate a novel design without a color uniformity issue in an illumination system. For reducing the lateral color aberration at the corner of the DMD active area, a novel ATIR prism is designed. We choose N-SF2 for the first prism and N-BK7 for the second prism. The lateral color aberration can be reduced to 0.48 μm. The spot sizes at the corner and the edge are controlled under 198 μm. We also get a compact prism size of 4091 mm3 with low cost.

For improving color uniformity at the center of the DMD active area, a light pipe with a suitable length is designed. The average Δu’v’ at the DMD active area can be controlled under 0.016 by a length of light pipe of 20 mm. We have controlled the color uniformity well. Moreover, illuminance uniformity at the DMD active area is higher than 92.8%. The illuminance distribution is uniform and flat. The optical efficiency of a light pipe is 94.1%. The over-filled efficiency is 90%.

We also simulate fabrication tolerances of an LED chip. When we shift the positions of red or blue LEDs from 0.05 mm to 0.30 mm, illumination uniformity at the DMD active area is still higher than 90.0% and the average Δu’v’ at the DMD active area remains under 0.016. Tolerance for the linear dimension can achieve a commercial level of ± 0.25 mm [19

19. W. J. Smith, “Prism and Mirror Systems,” in Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008), pp. 619–621.

]. Finally, a compact-size illumination system with an achromatic function is made by assembling the light pipe and the novel ATIR prism.

Acknowledgments

This study was supported by National Science Council projects 100-2220-E-009-022 and NSC99-2221-E-009-146 and in part by “Aim for the Top University Plan” of the National Chiao Tung University and Ministry of Education, Taiwan.

References and links

1.

E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science 308(5726), 1274–1278 (2005). [CrossRef] [PubMed]

2.

Texas Instruments (TI), “DLP® Discovery Optics 101 Application Note,” http://focus.ti.com/lit/an/dlpa022/dlpa022.pdf.

3.

H. Murat, D. Cuypers, H. De Smet, Y. Meuret, B. Van Giel, L. Bogaert, and H. Thienpont, “Two liquid crystal on silicon panel projector with efficient light-emitting diode illumination,” Opt. Eng. 46(12), 124002 (2007). [CrossRef]

4.

C.-M. Chang and H.-P. D. Shieh, “Design of illumination and projection optics for projectors with single digital micromirror devices,” Appl. Opt. 39(19), 3202–3208 (2000). [CrossRef] [PubMed]

5.

J.-W. Pan, S.-H. Tu, C.-M. Wang, and J.-Y. Chang, “High efficiency pocket-size projector with a compact projection lens and a light emitting diode-based light source system,” Appl. Opt. 47(19), 3406–3414 (2008). [CrossRef] [PubMed]

6.

G. Harbers, M. Keuper, and S. Paolini, “Performance of high power LED illuminators in color sequential projection displays,” in Proceedings of Internal Display Workshop (IDW 2003).

7.

G. Harbers, M. Keuper, and S. Paolini, “High power LED illuminators for data and video projector,” in Proceedings of Internal Display Workshop (IDW 2002).

8.

M. H. Keuper, G. Harbers, and S. Paolini, “RGB LED Illuminator for Pocket-sized Projectors,” in International Symposium Digest of Technical Papers (SID ’04), 943–945 (2004).

9.

M. Huseyin, C. Dieter, and D. S. Herbert, “Design of new collection systems for multi LED light engines,” Proc. SPIE 6196, 19604 (2006).

10.

J. W. Pan, C. M. Wang, H. C. Lan, W. S. Sun, and J. Y. Chang, “Homogenized LED-illumination using microlens arrays for a pocket-sized projector,” Opt. Express 15(17), 10483–10491 (2007). [CrossRef] [PubMed]

11.

E. H. Stupp and M. S. Brennesholtz, Projection Display, (Wiley, 2008).

12.

J. W. Pan, C. M. Wang, W. S. Sun, and J. Y. Chang, “Portable digital micromirror device projector using a prism,” Appl. Opt. 46(22), 5097–5102 (2007). [CrossRef] [PubMed]

13.

X. Zhao, Z.-L. Fang, J.-C. Cui, X. Zhang, and G.-G. Mu, “Illumination system using LED sources for pocket-size projectors,” Appl. Opt. 46(4), 522–526 (2007). [CrossRef] [PubMed]

14.

Zemax, http://www.zemax.com/.

15.

Ohara Corporation, “Optical Glass Cross Reference Sheet, http://www.oharacorp.com/catalog.html.

16.

G. W. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative data and Formulae, (John Wiley & Sons, 1982).

17.

OSRAM, “ LE_A_LE_T_LE_B_S2W,” http://catalog.osram-os.com/catalogue/catalogue.do?favOid=0000000400036fee03110023&act=showBookmark.

18.

LightTools, http://www.opticalres.com/.

19.

W. J. Smith, “Prism and Mirror Systems,” in Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008), pp. 619–621.

OCIS Codes
(220.4830) Optical design and fabrication : Systems design
(230.3670) Optical devices : Light-emitting diodes
(220.2945) Optical design and fabrication : Illumination design

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: May 23, 2011
Revised Manuscript: July 7, 2011
Manuscript Accepted: July 11, 2011
Published: August 2, 2011

Citation
Jui-Wen Pan and Sheng-Han Lin, "Achromatic design in the illumination system for a mini projector with LED light source," Opt. Express 19, 15750-15759 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-17-15750


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References

  1. E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science 308(5726), 1274–1278 (2005). [CrossRef] [PubMed]
  2. Texas Instruments (TI), “DLP® Discovery Optics 101 Application Note,” http://focus.ti.com/lit/an/dlpa022/dlpa022.pdf .
  3. H. Murat, D. Cuypers, H. De Smet, Y. Meuret, B. Van Giel, L. Bogaert, and H. Thienpont, “Two liquid crystal on silicon panel projector with efficient light-emitting diode illumination,” Opt. Eng. 46(12), 124002 (2007). [CrossRef]
  4. C.-M. Chang and H.-P. D. Shieh, “Design of illumination and projection optics for projectors with single digital micromirror devices,” Appl. Opt. 39(19), 3202–3208 (2000). [CrossRef] [PubMed]
  5. J.-W. Pan, S.-H. Tu, C.-M. Wang, and J.-Y. Chang, “High efficiency pocket-size projector with a compact projection lens and a light emitting diode-based light source system,” Appl. Opt. 47(19), 3406–3414 (2008). [CrossRef] [PubMed]
  6. G. Harbers, M. Keuper, and S. Paolini, “Performance of high power LED illuminators in color sequential projection displays,” in Proceedings of Internal Display Workshop (IDW 2003).
  7. G. Harbers, M. Keuper, and S. Paolini, “High power LED illuminators for data and video projector,” in Proceedings of Internal Display Workshop (IDW 2002).
  8. M. H. Keuper, G. Harbers, and S. Paolini, “RGB LED Illuminator for Pocket-sized Projectors,” in International Symposium Digest of Technical Papers (SID ’04), 943–945 (2004).
  9. M. Huseyin, C. Dieter, and D. S. Herbert, “Design of new collection systems for multi LED light engines,” Proc. SPIE 6196, 19604 (2006).
  10. J. W. Pan, C. M. Wang, H. C. Lan, W. S. Sun, and J. Y. Chang, “Homogenized LED-illumination using microlens arrays for a pocket-sized projector,” Opt. Express 15(17), 10483–10491 (2007). [CrossRef] [PubMed]
  11. E. H. Stupp and M. S. Brennesholtz, Projection Display, (Wiley, 2008).
  12. J. W. Pan, C. M. Wang, W. S. Sun, and J. Y. Chang, “Portable digital micromirror device projector using a prism,” Appl. Opt. 46(22), 5097–5102 (2007). [CrossRef] [PubMed]
  13. X. Zhao, Z.-L. Fang, J.-C. Cui, X. Zhang, and G.-G. Mu, “Illumination system using LED sources for pocket-size projectors,” Appl. Opt. 46(4), 522–526 (2007). [CrossRef] [PubMed]
  14. Zemax, http://www.zemax.com/ .
  15. Ohara Corporation, “Optical Glass Cross Reference Sheet, http://www.oharacorp.com/catalog.html .
  16. G. W. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative data and Formulae, (John Wiley & Sons, 1982).
  17. OSRAM, “ LE_A_LE_T_LE_B_S2W,” http://catalog.osram-os.com/catalogue/catalogue.do?favOid=0000000400036fee03110023&act=showBookmark .
  18. LightTools, http://www.opticalres.com/ .
  19. W. J. Smith, “Prism and Mirror Systems,” in Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008), pp. 619–621.

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