Abstract

We investigate a novel light source design for efficient collection of UV light from multiple LEDs. The design is based on a truncated cone with a large circular lid incorporating LEDs on one side, and a small circular exit aperture (diameter of 9 mm) on the other side. The exit aperture size allows a simple coupling with secondary optics of a microscope for hyperspectral imaging that requires a wide spectrum of frequencies of illuminating light. The light collection efficiency was optimized with respect to cone length and diameter of the LED lid. In all simulations, we use a highly UV-reflecting aluminum coating on the inner surfaces of the cone. The influence of the LED positions on the cone efficiency is determined by varying the LED distance from the central axis as well as the interLED distance. We found the maximum efficiency of the cone is realized for LEDs positioned at the center, and the shorter is the inter-LED distance, the better is the performance of the light source.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. M. E. Gosnell, A. G. Anwer, J. C. Cassano, C. M. Sue, and E. M. Goldys, “Functional hyperspectral imaging captures subtle details of cell metabolism in olfactory neurosphere cells, disease-specific models of neurodegenerative disorders,” Biochimica et Biophysica Acta (BBA) - Molecular Cell Research 1863(1), 56–63 (2016).
  2. M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).
  3. T. E. Renkoski, B. Banerjee, L. R. Graves, N. S. Rial, S. A. H. Reid, V. L. Tsikitis, V. N. Nfonsam, P. Tiwari, H. Gavini, and U. Utzinger, “Ratio images and ultraviolet C excitation in autofluorescence imaging of neoplasms of the human colon,” J. Biomed. Opt. 18(1), 16005 (2013).
    [PubMed]
  4. R. W. Cole and J. N. Turner, “Light-Emitting Diodes Are Better Illumination Sources for Biological Microscopy than Conventional Sources,” Microsc. Microanal. 14(3), 243–250 (2008).
    [PubMed]
  5. B. Hohman, “LED light source: Major advance in fluorescence microscopy,” Biomed. Instrum. Technol. 41(6), 461–464 (2007).
    [PubMed]
  6. I. Young, Y. Garini, H. Dietrich, W. van Oel, and G. Lung, “LEDs for fluorescence microscopy,” Proc. SPIE 5324, 208–215 (2004).
  7. K. Balasubramanian, J. Hennessy, N. Raouf, S. Nikzad, M. Ayala, S. Shaklan, P. Scowen, J. Del Hoyo and M. Quijada, “Aluminum mirror coatings for UVOIR telescope optics including the far UV,”Proc. SPIE 9602, 96020I96021–96029 (2015).
  8. I. Lindseth, A. Bardal, and R. Spooren, “Reflectance measurements of aluminium surfaces using integrating spheres,” Opt. Lasers Eng. 32(5), 419–435 (1999).
  9. I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt. 45(10), 2265–2272 (2006).
    [PubMed]
  10. K. K. Li, S. Inatsugu, and S. Sillyman, “Design and optimization of tapered light pipes,” Proc. SPIE 5529, 48–57 (2004).
  11. C.-C. Sun, I. Moreno, Y.-C. Lo, B.-C. Chiu, and W.-T. Chien, “Collimating lamp with well color mixing of red/green/blue LEDs,” Opt. Express 20(1S1), A75–A84 (2012).
    [PubMed]
  12. F. J. Bolton, A. Bernat, S. L. Jacques and D. Levitz, “Development and testing of a homogenous multi-wavelength LED light source,”Proc. SPIE 10055, 100550R (2017).
  13. C. Chen and X. Zhang, “Design of optical system for collimating the light of an LED uniformly,” J. Opt. Soc. Am. A 31(5), 1118–1125 (2014).
    [PubMed]

2016 (1)

M. E. Gosnell, A. G. Anwer, J. C. Cassano, C. M. Sue, and E. M. Goldys, “Functional hyperspectral imaging captures subtle details of cell metabolism in olfactory neurosphere cells, disease-specific models of neurodegenerative disorders,” Biochimica et Biophysica Acta (BBA) - Molecular Cell Research 1863(1), 56–63 (2016).

2014 (1)

2013 (1)

T. E. Renkoski, B. Banerjee, L. R. Graves, N. S. Rial, S. A. H. Reid, V. L. Tsikitis, V. N. Nfonsam, P. Tiwari, H. Gavini, and U. Utzinger, “Ratio images and ultraviolet C excitation in autofluorescence imaging of neoplasms of the human colon,” J. Biomed. Opt. 18(1), 16005 (2013).
[PubMed]

2012 (1)

2008 (1)

R. W. Cole and J. N. Turner, “Light-Emitting Diodes Are Better Illumination Sources for Biological Microscopy than Conventional Sources,” Microsc. Microanal. 14(3), 243–250 (2008).
[PubMed]

2007 (1)

B. Hohman, “LED light source: Major advance in fluorescence microscopy,” Biomed. Instrum. Technol. 41(6), 461–464 (2007).
[PubMed]

2006 (1)

2004 (2)

K. K. Li, S. Inatsugu, and S. Sillyman, “Design and optimization of tapered light pipes,” Proc. SPIE 5529, 48–57 (2004).

I. Young, Y. Garini, H. Dietrich, W. van Oel, and G. Lung, “LEDs for fluorescence microscopy,” Proc. SPIE 5324, 208–215 (2004).

1999 (1)

I. Lindseth, A. Bardal, and R. Spooren, “Reflectance measurements of aluminium surfaces using integrating spheres,” Opt. Lasers Eng. 32(5), 419–435 (1999).

Adhikary, P. P.

M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).

Anwer, A. G.

M. E. Gosnell, A. G. Anwer, J. C. Cassano, C. M. Sue, and E. M. Goldys, “Functional hyperspectral imaging captures subtle details of cell metabolism in olfactory neurosphere cells, disease-specific models of neurodegenerative disorders,” Biochimica et Biophysica Acta (BBA) - Molecular Cell Research 1863(1), 56–63 (2016).

M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).

Avendaño-Alejo, M.

Banerjee, B.

T. E. Renkoski, B. Banerjee, L. R. Graves, N. S. Rial, S. A. H. Reid, V. L. Tsikitis, V. N. Nfonsam, P. Tiwari, H. Gavini, and U. Utzinger, “Ratio images and ultraviolet C excitation in autofluorescence imaging of neoplasms of the human colon,” J. Biomed. Opt. 18(1), 16005 (2013).
[PubMed]

Bardal, A.

I. Lindseth, A. Bardal, and R. Spooren, “Reflectance measurements of aluminium surfaces using integrating spheres,” Opt. Lasers Eng. 32(5), 419–435 (1999).

Cahill, M. A.

M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).

Cassano, J. C.

M. E. Gosnell, A. G. Anwer, J. C. Cassano, C. M. Sue, and E. M. Goldys, “Functional hyperspectral imaging captures subtle details of cell metabolism in olfactory neurosphere cells, disease-specific models of neurodegenerative disorders,” Biochimica et Biophysica Acta (BBA) - Molecular Cell Research 1863(1), 56–63 (2016).

Chen, C.

Chien, W.-T.

Chiu, B.-C.

Cole, R. W.

R. W. Cole and J. N. Turner, “Light-Emitting Diodes Are Better Illumination Sources for Biological Microscopy than Conventional Sources,” Microsc. Microanal. 14(3), 243–250 (2008).
[PubMed]

Dietrich, H.

I. Young, Y. Garini, H. Dietrich, W. van Oel, and G. Lung, “LEDs for fluorescence microscopy,” Proc. SPIE 5324, 208–215 (2004).

Garini, Y.

I. Young, Y. Garini, H. Dietrich, W. van Oel, and G. Lung, “LEDs for fluorescence microscopy,” Proc. SPIE 5324, 208–215 (2004).

Gavini, H.

T. E. Renkoski, B. Banerjee, L. R. Graves, N. S. Rial, S. A. H. Reid, V. L. Tsikitis, V. N. Nfonsam, P. Tiwari, H. Gavini, and U. Utzinger, “Ratio images and ultraviolet C excitation in autofluorescence imaging of neoplasms of the human colon,” J. Biomed. Opt. 18(1), 16005 (2013).
[PubMed]

Goldys, E. M.

M. E. Gosnell, A. G. Anwer, J. C. Cassano, C. M. Sue, and E. M. Goldys, “Functional hyperspectral imaging captures subtle details of cell metabolism in olfactory neurosphere cells, disease-specific models of neurodegenerative disorders,” Biochimica et Biophysica Acta (BBA) - Molecular Cell Research 1863(1), 56–63 (2016).

M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).

Gosnell, M. E.

M. E. Gosnell, A. G. Anwer, J. C. Cassano, C. M. Sue, and E. M. Goldys, “Functional hyperspectral imaging captures subtle details of cell metabolism in olfactory neurosphere cells, disease-specific models of neurodegenerative disorders,” Biochimica et Biophysica Acta (BBA) - Molecular Cell Research 1863(1), 56–63 (2016).

M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).

Graves, L. R.

T. E. Renkoski, B. Banerjee, L. R. Graves, N. S. Rial, S. A. H. Reid, V. L. Tsikitis, V. N. Nfonsam, P. Tiwari, H. Gavini, and U. Utzinger, “Ratio images and ultraviolet C excitation in autofluorescence imaging of neoplasms of the human colon,” J. Biomed. Opt. 18(1), 16005 (2013).
[PubMed]

Hohman, B.

B. Hohman, “LED light source: Major advance in fluorescence microscopy,” Biomed. Instrum. Technol. 41(6), 461–464 (2007).
[PubMed]

Inatsugu, S.

K. K. Li, S. Inatsugu, and S. Sillyman, “Design and optimization of tapered light pipes,” Proc. SPIE 5529, 48–57 (2004).

Inglis, D. W.

M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).

Jazayeri, J. A.

M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).

Li, K. K.

K. K. Li, S. Inatsugu, and S. Sillyman, “Design and optimization of tapered light pipes,” Proc. SPIE 5529, 48–57 (2004).

Lindseth, I.

I. Lindseth, A. Bardal, and R. Spooren, “Reflectance measurements of aluminium surfaces using integrating spheres,” Opt. Lasers Eng. 32(5), 419–435 (1999).

Lo, Y.-C.

Lung, G.

I. Young, Y. Garini, H. Dietrich, W. van Oel, and G. Lung, “LEDs for fluorescence microscopy,” Proc. SPIE 5324, 208–215 (2004).

Mahbub, S. B.

M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).

Menon Perinchery, S.

M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).

Moreno, I.

Nfonsam, V. N.

T. E. Renkoski, B. Banerjee, L. R. Graves, N. S. Rial, S. A. H. Reid, V. L. Tsikitis, V. N. Nfonsam, P. Tiwari, H. Gavini, and U. Utzinger, “Ratio images and ultraviolet C excitation in autofluorescence imaging of neoplasms of the human colon,” J. Biomed. Opt. 18(1), 16005 (2013).
[PubMed]

Pollock, C. A.

M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).

Reid, S. A. H.

T. E. Renkoski, B. Banerjee, L. R. Graves, N. S. Rial, S. A. H. Reid, V. L. Tsikitis, V. N. Nfonsam, P. Tiwari, H. Gavini, and U. Utzinger, “Ratio images and ultraviolet C excitation in autofluorescence imaging of neoplasms of the human colon,” J. Biomed. Opt. 18(1), 16005 (2013).
[PubMed]

Renkoski, T. E.

T. E. Renkoski, B. Banerjee, L. R. Graves, N. S. Rial, S. A. H. Reid, V. L. Tsikitis, V. N. Nfonsam, P. Tiwari, H. Gavini, and U. Utzinger, “Ratio images and ultraviolet C excitation in autofluorescence imaging of neoplasms of the human colon,” J. Biomed. Opt. 18(1), 16005 (2013).
[PubMed]

Rial, N. S.

T. E. Renkoski, B. Banerjee, L. R. Graves, N. S. Rial, S. A. H. Reid, V. L. Tsikitis, V. N. Nfonsam, P. Tiwari, H. Gavini, and U. Utzinger, “Ratio images and ultraviolet C excitation in autofluorescence imaging of neoplasms of the human colon,” J. Biomed. Opt. 18(1), 16005 (2013).
[PubMed]

Saad, S.

M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).

Sillyman, S.

K. K. Li, S. Inatsugu, and S. Sillyman, “Design and optimization of tapered light pipes,” Proc. SPIE 5529, 48–57 (2004).

Spooren, R.

I. Lindseth, A. Bardal, and R. Spooren, “Reflectance measurements of aluminium surfaces using integrating spheres,” Opt. Lasers Eng. 32(5), 419–435 (1999).

Sue, C. M.

M. E. Gosnell, A. G. Anwer, J. C. Cassano, C. M. Sue, and E. M. Goldys, “Functional hyperspectral imaging captures subtle details of cell metabolism in olfactory neurosphere cells, disease-specific models of neurodegenerative disorders,” Biochimica et Biophysica Acta (BBA) - Molecular Cell Research 1863(1), 56–63 (2016).

Sun, C.-C.

Sutton-McDowall, M. L.

M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).

Thompson, J. G.

M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).

Tiwari, P.

T. E. Renkoski, B. Banerjee, L. R. Graves, N. S. Rial, S. A. H. Reid, V. L. Tsikitis, V. N. Nfonsam, P. Tiwari, H. Gavini, and U. Utzinger, “Ratio images and ultraviolet C excitation in autofluorescence imaging of neoplasms of the human colon,” J. Biomed. Opt. 18(1), 16005 (2013).
[PubMed]

Tsikitis, V. L.

T. E. Renkoski, B. Banerjee, L. R. Graves, N. S. Rial, S. A. H. Reid, V. L. Tsikitis, V. N. Nfonsam, P. Tiwari, H. Gavini, and U. Utzinger, “Ratio images and ultraviolet C excitation in autofluorescence imaging of neoplasms of the human colon,” J. Biomed. Opt. 18(1), 16005 (2013).
[PubMed]

Turner, J. N.

R. W. Cole and J. N. Turner, “Light-Emitting Diodes Are Better Illumination Sources for Biological Microscopy than Conventional Sources,” Microsc. Microanal. 14(3), 243–250 (2008).
[PubMed]

Tzonchev, R. I.

Utzinger, U.

T. E. Renkoski, B. Banerjee, L. R. Graves, N. S. Rial, S. A. H. Reid, V. L. Tsikitis, V. N. Nfonsam, P. Tiwari, H. Gavini, and U. Utzinger, “Ratio images and ultraviolet C excitation in autofluorescence imaging of neoplasms of the human colon,” J. Biomed. Opt. 18(1), 16005 (2013).
[PubMed]

van Oel, W.

I. Young, Y. Garini, H. Dietrich, W. van Oel, and G. Lung, “LEDs for fluorescence microscopy,” Proc. SPIE 5324, 208–215 (2004).

Young, I.

I. Young, Y. Garini, H. Dietrich, W. van Oel, and G. Lung, “LEDs for fluorescence microscopy,” Proc. SPIE 5324, 208–215 (2004).

Zhang, X.

Appl. Opt. (1)

Biochimica et Biophysica Acta (BBA) - Molecular Cell Research (1)

M. E. Gosnell, A. G. Anwer, J. C. Cassano, C. M. Sue, and E. M. Goldys, “Functional hyperspectral imaging captures subtle details of cell metabolism in olfactory neurosphere cells, disease-specific models of neurodegenerative disorders,” Biochimica et Biophysica Acta (BBA) - Molecular Cell Research 1863(1), 56–63 (2016).

Biomed. Instrum. Technol. (1)

B. Hohman, “LED light source: Major advance in fluorescence microscopy,” Biomed. Instrum. Technol. 41(6), 461–464 (2007).
[PubMed]

J. Biomed. Opt. (1)

T. E. Renkoski, B. Banerjee, L. R. Graves, N. S. Rial, S. A. H. Reid, V. L. Tsikitis, V. N. Nfonsam, P. Tiwari, H. Gavini, and U. Utzinger, “Ratio images and ultraviolet C excitation in autofluorescence imaging of neoplasms of the human colon,” J. Biomed. Opt. 18(1), 16005 (2013).
[PubMed]

J. Opt. Soc. Am. A (1)

Microsc. Microanal. (1)

R. W. Cole and J. N. Turner, “Light-Emitting Diodes Are Better Illumination Sources for Biological Microscopy than Conventional Sources,” Microsc. Microanal. 14(3), 243–250 (2008).
[PubMed]

Opt. Express (1)

Opt. Lasers Eng. (1)

I. Lindseth, A. Bardal, and R. Spooren, “Reflectance measurements of aluminium surfaces using integrating spheres,” Opt. Lasers Eng. 32(5), 419–435 (1999).

Proc. SPIE (2)

K. K. Li, S. Inatsugu, and S. Sillyman, “Design and optimization of tapered light pipes,” Proc. SPIE 5529, 48–57 (2004).

I. Young, Y. Garini, H. Dietrich, W. van Oel, and G. Lung, “LEDs for fluorescence microscopy,” Proc. SPIE 5324, 208–215 (2004).

Other (3)

K. Balasubramanian, J. Hennessy, N. Raouf, S. Nikzad, M. Ayala, S. Shaklan, P. Scowen, J. Del Hoyo and M. Quijada, “Aluminum mirror coatings for UVOIR telescope optics including the far UV,”Proc. SPIE 9602, 96020I96021–96029 (2015).

F. J. Bolton, A. Bernat, S. L. Jacques and D. Levitz, “Development and testing of a homogenous multi-wavelength LED light source,”Proc. SPIE 10055, 100550R (2017).

M. E. Gosnell, A. G. Anwer, S. B. Mahbub, S. Menon Perinchery, D. W. Inglis, P. P. Adhikary, J. A. Jazayeri, M. A. Cahill, S. Saad, C. A. Pollock, M. L. Sutton-McDowall, J. G. Thompson, and E. M. Goldys, “Quantitative non-invasive cell characterisation and discrimination based on multispectral autofluorescence features,” 6 (1), 1–11 (2016).

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Figures (9)

Fig. 1
Fig. 1

(A). Schematics of a truncated cone light source. (B). Truncated cone light source combined with the secondary optics of Hg lamp in an inverted microscope.

Fig. 2
Fig. 2

Variation of reflectance with the angle of incidence on aluminum coating.

Fig. 3
Fig. 3

Model of truncated cone with 13 LEDs.

Fig. 4
Fig. 4

Optical efficiency has been plotted against diameter/Length (D/L) ratio of truncated cone for different cone lengths (CL) ranging from 50 mm to 250 mm. The figure indicates that for D/L = 1, the shortest length of cone produces the highest optical efficiency.

Fig. 5
Fig. 5

The flux components of two LEDs, separated by interLED distance of 5mm and 20mm have been shown. The bar chart indicates that the most of rays are incident on slanting sides of cone and cone lid. In particular, for two LEDs, large interLED distance (20mm) causes more loss of rays (presented in dark green) as compared to small interLED distance (5mm).

Fig. 6
Fig. 6

Variation of source efficiency in a cone as a function of distance of single LED from the center. Cone thickness is 1mm, L = 60 mm, D/2 = 30 mm, standard model conditions (Al-mirror coating, 250,000 ray tracing, d = 9mm) are maintained in this study.

Fig. 7
Fig. 7

The LEDs number and interLED distance affect efficiency of cone. The efficiency decreases with increase in the number of LEDs and larger gaps between LEDs. Under standard model conditions (Al-mirror coating, d = 9mm), 10000 rays per LED are traced for 13 LEDs, cone thickness is 1mm, L = 60 mm, D/2 = 30 mm.

Fig. 8
Fig. 8

The irradiance profile of optical efficiency has been found shifting with change in the position of illuminating LEDs at the lid of an optimized cone, L = 60 mm, D/2 = 30 mm, Al mirror coating, 250,000 ray traces, d = 9mm, cone thickness = 1mm, 1 LED is positioned at the center (A) and 20mm off axis (-x, -y, + x, + y axes in figures B, C, D, E respectively).

Fig. 9
Fig. 9

The optical output of the cone shows variation with the increase in tilt and distance of LED with respect to the central axis of truncated cone. For smaller LED tilts (0 to 50°) and distances from central axis (5mm), the optical output is more. Whereas, for the LED tilt higher than 50 degree the output starts decreasing for the same position of LED.

Equations (1)

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