Abstract

Two-dimensional binary diffraction gratings can be used in wearable display applications as exit-pupil expanders (EPEs) (or numerical-aperture expanders) to increase the size of the display exit pupil. In retinal scanning displays the EPE is placed at an intermediate image plane between the scanners and the display exit pupil. A focused spot scans across the diffractive EPE and produces multiple diffraction orders at the exit pupil. The overall luminance uniformity across the exit pupil as perceived by the viewer is a function of the uniformity of the diffraction-order intensities, focused-spot size, grating period, scanning-beam profile, and the viewer’s eye-pupil size. The design, the diffraction-order uniformity, and the effects of the grating phase angle on the uniformity for binary diffraction gratings are discussed. Also discussed are the display exit-pupil uniformity and the impact of the diffractive EPE on the point-spread function and the modulation transfer function of the display. Both theoretical and experimental results are presented.

© 2001 Optical Society of America

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References

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  1. H. L. Task, “HMD image source, optics, and the visual interface,” in Head Mounted Displays: Designing for the User, J. E. Melzer, K. Moffitt, eds. (McGraw-Hill, New York, 1997), Chap. 3, pp. 55–82.
  2. C. E. Rash, ed., Helmet-Mounted Displays: Design Issues for Rotary-Wing Aircraft, Vol. PM93 of SPIE Monographs and Handbooks Series (SPIE Press, Bellingham, Wash., 2001).
  3. H. Urey, “Retinal scanning displays,” in Encyclopedia of Optical Engineering, R. B. Johnson, R. G. Diggers, eds. (Marcel Dekker, New York, 2001).
  4. H. Urey, N. Nestorovic, B. Ng, A. Gross, “Optics designs and system MTF for laser scanning displays,” in Helmet and Head-Mounted Displays IV, R. J. Lewandowski, L. A. Haworth, H. J. Girolamo, eds., Proc. SPIE3689, 238–248 (1999).
    [CrossRef]
  5. H. Urey, D. W. Wine, T. D. Osborn, “Optical performance requirements for MEMS-scanner based microdisplays,” in MOEMS and Miniaturized Systems, M. E. Motamedi, R. Göring, eds., Proc. SPIE4178, 176–185 (2000).
    [CrossRef]
  6. A. Stevens, H. Urey, P. Lopez, T. R. M. Sales, R. McGuire, D. H. Raguin, “Diffractive optical elements for numerical aperture expansion in retinal scanning displays,” in DiffractiveOptics and Micro-Optics, Vol. 41 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 316–318.
  7. M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, N. Ross, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
    [CrossRef]
  8. H. Dammann, K. Gortler, “High efficiency in line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
    [CrossRef]
  9. J. Turunen, M. Kuittinen, F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1999), Vol. XL, Chap. 5, pp. 341–387.
  10. P. Blair, H. Lpken, M. R. Taghizadeh, F. Wyrowski, “Multilevel phase-only array generators with a trapezoidal phase topology,” Appl. Opt. 36, 4713–4721 (1997).
    [CrossRef] [PubMed]
  11. W. Daschner, P. Long, R. Stein, C. Wu, S. H. Lee, “Cost-effective mass fabrication of multilevel diffractive optical elements by use of a single optical exposure with a gray-scale mask on high-energy beam-sensitive glass,” Appl. Opt. 36, 4675–4680 (1997).
    [CrossRef] [PubMed]
  12. Holomaster II software, Flexible Optical, BV ( http://www.okotech.com/hm/index.html ).
  13. S. Kirkpatrick, C. Gelatt, J. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
    [CrossRef] [PubMed]
  14. W. Lee, “High efficiency multiple beam gratings,” Appl. Opt. 18, 2152–2157 (1979).
    [CrossRef] [PubMed]
  15. J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
    [CrossRef]
  16. H. Urey, “Diffraction limited resolution and maximum contrast for scanning displays,” in 2000 SID International Symposium Technical Digest of Papers (Society of Information Display, San Jose, Calif., 2000), Vol. XXXI, pp. 866–869.
    [CrossRef]

1997 (3)

1989 (1)

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

1983 (1)

S. Kirkpatrick, C. Gelatt, J. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

1979 (1)

1971 (1)

H. Dammann, K. Gortler, “High efficiency in line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Barton, I. M.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, N. Ross, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
[CrossRef]

Blair, P.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, N. Ross, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
[CrossRef]

P. Blair, H. Lpken, M. R. Taghizadeh, F. Wyrowski, “Multilevel phase-only array generators with a trapezoidal phase topology,” Appl. Opt. 36, 4713–4721 (1997).
[CrossRef] [PubMed]

Dammann, H.

H. Dammann, K. Gortler, “High efficiency in line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Daschner, W.

Downs, M. M.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Gelatt, C.

S. Kirkpatrick, C. Gelatt, J. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Gortler, K.

H. Dammann, K. Gortler, “High efficiency in line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Gross, A.

H. Urey, N. Nestorovic, B. Ng, A. Gross, “Optics designs and system MTF for laser scanning displays,” in Helmet and Head-Mounted Displays IV, R. J. Lewandowski, L. A. Haworth, H. J. Girolamo, eds., Proc. SPIE3689, 238–248 (1999).
[CrossRef]

Jahns, J.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, C. Gelatt, J. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Kuittinen, M.

J. Turunen, M. Kuittinen, F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1999), Vol. XL, Chap. 5, pp. 341–387.

Layet, B.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, N. Ross, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
[CrossRef]

Lee, S. H.

Lee, W.

Long, P.

Lopez, P.

A. Stevens, H. Urey, P. Lopez, T. R. M. Sales, R. McGuire, D. H. Raguin, “Diffractive optical elements for numerical aperture expansion in retinal scanning displays,” in DiffractiveOptics and Micro-Optics, Vol. 41 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 316–318.

Lpken, H.

McGuire, R.

A. Stevens, H. Urey, P. Lopez, T. R. M. Sales, R. McGuire, D. H. Raguin, “Diffractive optical elements for numerical aperture expansion in retinal scanning displays,” in DiffractiveOptics and Micro-Optics, Vol. 41 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 316–318.

Nestorovic, N.

H. Urey, N. Nestorovic, B. Ng, A. Gross, “Optics designs and system MTF for laser scanning displays,” in Helmet and Head-Mounted Displays IV, R. J. Lewandowski, L. A. Haworth, H. J. Girolamo, eds., Proc. SPIE3689, 238–248 (1999).
[CrossRef]

Ng, B.

H. Urey, N. Nestorovic, B. Ng, A. Gross, “Optics designs and system MTF for laser scanning displays,” in Helmet and Head-Mounted Displays IV, R. J. Lewandowski, L. A. Haworth, H. J. Girolamo, eds., Proc. SPIE3689, 238–248 (1999).
[CrossRef]

Osborn, T. D.

H. Urey, D. W. Wine, T. D. Osborn, “Optical performance requirements for MEMS-scanner based microdisplays,” in MOEMS and Miniaturized Systems, M. E. Motamedi, R. Göring, eds., Proc. SPIE4178, 176–185 (2000).
[CrossRef]

Prise, M. E.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Raguin, D. H.

A. Stevens, H. Urey, P. Lopez, T. R. M. Sales, R. McGuire, D. H. Raguin, “Diffractive optical elements for numerical aperture expansion in retinal scanning displays,” in DiffractiveOptics and Micro-Optics, Vol. 41 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 316–318.

Ross, N.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, N. Ross, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
[CrossRef]

Sales, T. R. M.

A. Stevens, H. Urey, P. Lopez, T. R. M. Sales, R. McGuire, D. H. Raguin, “Diffractive optical elements for numerical aperture expansion in retinal scanning displays,” in DiffractiveOptics and Micro-Optics, Vol. 41 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 316–318.

Stein, R.

Stevens, A.

A. Stevens, H. Urey, P. Lopez, T. R. M. Sales, R. McGuire, D. H. Raguin, “Diffractive optical elements for numerical aperture expansion in retinal scanning displays,” in DiffractiveOptics and Micro-Optics, Vol. 41 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 316–318.

Streibl, N.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Taghizadeh, M. R.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, N. Ross, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
[CrossRef]

P. Blair, H. Lpken, M. R. Taghizadeh, F. Wyrowski, “Multilevel phase-only array generators with a trapezoidal phase topology,” Appl. Opt. 36, 4713–4721 (1997).
[CrossRef] [PubMed]

Task, H. L.

H. L. Task, “HMD image source, optics, and the visual interface,” in Head Mounted Displays: Designing for the User, J. E. Melzer, K. Moffitt, eds. (McGraw-Hill, New York, 1997), Chap. 3, pp. 55–82.

Turunen, J.

J. Turunen, M. Kuittinen, F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1999), Vol. XL, Chap. 5, pp. 341–387.

Urey, H.

H. Urey, “Diffraction limited resolution and maximum contrast for scanning displays,” in 2000 SID International Symposium Technical Digest of Papers (Society of Information Display, San Jose, Calif., 2000), Vol. XXXI, pp. 866–869.
[CrossRef]

H. Urey, D. W. Wine, T. D. Osborn, “Optical performance requirements for MEMS-scanner based microdisplays,” in MOEMS and Miniaturized Systems, M. E. Motamedi, R. Göring, eds., Proc. SPIE4178, 176–185 (2000).
[CrossRef]

H. Urey, “Retinal scanning displays,” in Encyclopedia of Optical Engineering, R. B. Johnson, R. G. Diggers, eds. (Marcel Dekker, New York, 2001).

A. Stevens, H. Urey, P. Lopez, T. R. M. Sales, R. McGuire, D. H. Raguin, “Diffractive optical elements for numerical aperture expansion in retinal scanning displays,” in DiffractiveOptics and Micro-Optics, Vol. 41 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 316–318.

H. Urey, N. Nestorovic, B. Ng, A. Gross, “Optics designs and system MTF for laser scanning displays,” in Helmet and Head-Mounted Displays IV, R. J. Lewandowski, L. A. Haworth, H. J. Girolamo, eds., Proc. SPIE3689, 238–248 (1999).
[CrossRef]

Vecchi, J.

S. Kirkpatrick, C. Gelatt, J. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Waddie, A. J.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, N. Ross, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
[CrossRef]

Walker, S. J.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Wine, D. W.

H. Urey, D. W. Wine, T. D. Osborn, “Optical performance requirements for MEMS-scanner based microdisplays,” in MOEMS and Miniaturized Systems, M. E. Motamedi, R. Göring, eds., Proc. SPIE4178, 176–185 (2000).
[CrossRef]

Wu, C.

Wyrowski, F.

P. Blair, H. Lpken, M. R. Taghizadeh, F. Wyrowski, “Multilevel phase-only array generators with a trapezoidal phase topology,” Appl. Opt. 36, 4713–4721 (1997).
[CrossRef] [PubMed]

J. Turunen, M. Kuittinen, F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1999), Vol. XL, Chap. 5, pp. 341–387.

Appl. Opt. (3)

Microelectron. Eng. (1)

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, N. Ross, “Design and fabrication of diffractive optical elements,” Microelectron. Eng. 34, 219–242 (1997).
[CrossRef]

Opt. Commun. (1)

H. Dammann, K. Gortler, “High efficiency in line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Opt. Eng. (1)

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Science (1)

S. Kirkpatrick, C. Gelatt, J. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Other (9)

H. Urey, “Diffraction limited resolution and maximum contrast for scanning displays,” in 2000 SID International Symposium Technical Digest of Papers (Society of Information Display, San Jose, Calif., 2000), Vol. XXXI, pp. 866–869.
[CrossRef]

J. Turunen, M. Kuittinen, F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in Optics, E. Wolf, ed. (Elsevier, New York, 1999), Vol. XL, Chap. 5, pp. 341–387.

Holomaster II software, Flexible Optical, BV ( http://www.okotech.com/hm/index.html ).

H. L. Task, “HMD image source, optics, and the visual interface,” in Head Mounted Displays: Designing for the User, J. E. Melzer, K. Moffitt, eds. (McGraw-Hill, New York, 1997), Chap. 3, pp. 55–82.

C. E. Rash, ed., Helmet-Mounted Displays: Design Issues for Rotary-Wing Aircraft, Vol. PM93 of SPIE Monographs and Handbooks Series (SPIE Press, Bellingham, Wash., 2001).

H. Urey, “Retinal scanning displays,” in Encyclopedia of Optical Engineering, R. B. Johnson, R. G. Diggers, eds. (Marcel Dekker, New York, 2001).

H. Urey, N. Nestorovic, B. Ng, A. Gross, “Optics designs and system MTF for laser scanning displays,” in Helmet and Head-Mounted Displays IV, R. J. Lewandowski, L. A. Haworth, H. J. Girolamo, eds., Proc. SPIE3689, 238–248 (1999).
[CrossRef]

H. Urey, D. W. Wine, T. D. Osborn, “Optical performance requirements for MEMS-scanner based microdisplays,” in MOEMS and Miniaturized Systems, M. E. Motamedi, R. Göring, eds., Proc. SPIE4178, 176–185 (2000).
[CrossRef]

A. Stevens, H. Urey, P. Lopez, T. R. M. Sales, R. McGuire, D. H. Raguin, “Diffractive optical elements for numerical aperture expansion in retinal scanning displays,” in DiffractiveOptics and Micro-Optics, Vol. 41 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 316–318.

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Figures (16)

Fig. 1
Fig. 1

Cross section of the optical layout for a RSD from light source to the viewer’s eye, illustrating the EPE operation. P ep, exit-pupil size of the display; L, intermediate image size; N, number of pixels; p, pixel size; D, scan mirror size; θTOSA, total optical scan angle; θ i , EPE input-beam angle; θ0, EPE output-beam angle; e, eye-pupil size.

Fig. 2
Fig. 2

(a) Far-field pattern created by a diffractive EPE when illuminated with a collimated laser beam that is much larger than the EPE grating period. (b) Typical exit-pupil pattern created by the same diffractive EPE used for (a) in a RSD system when illuminated with a focused beam scanning across the element.

Fig. 3
Fig. 3

(a) Desired 11 × 11 circular diffraction-order intensity pattern. (b) The resultant diffraction-order intensities for the design in (c). The binary phase-grating designs in (c) and (d) were obtained by use of the Halomaster II diffractive optical element design software,12 and both designs result in nearly identical diffraction-order intensity patterns.

Fig. 4
Fig. 4

(a) Repeated binary grating-cell design for an exemplary EPE and (b) a cross-sectional view of the cell.

Fig. 5
Fig. 5

Ratio of the zeroth-order intensity to the average diffraction-order intensity I 0/I avg plotted as a function of the percent etch-depth error ε. Assumptions are that there are N epe = 121 diffraction orders within the intended circular NA, the diffraction efficiency is η = 75%, the refractive index is n = 1.46, A 1 = 0.53d 2, and A 0 = 0.47d 2, producing I 0/I avg = 1 for ε = 0.

Fig. 6
Fig. 6

Theoretical and measurement results for I 0 and measurement results for one of the off-axis–order intensities plotted as functions of the beam’s incidence angle at the EPE. All values are relative to the average diffraction-order intensity of 1.0. Assumptions for Fig. 6 are the same as those for Fig. 5.

Fig. 7
Fig. 7

RSD focusing geometry and EPE operation illustrating Gaussian beam truncation at the limiting system aperture. w m , the 1/e 2-intensity beam radius; d, the grating period.

Fig. 8
Fig. 8

Experimental results for the exit-pupil pattern as a function of the spot-size–to–cell-size ratio s/ d. Changing the NA of the focusing geometry varies the s/ d ratio.

Fig. 9
Fig. 9

Exit-pupil patterns produced by two different beam profiles at the system aperture (the aperture size is adjusted to yield the same FWHM spot size in each case): (a) small truncation (Gaussian beam and Gaussian spot) and (b) large truncation (uniform beam and Airy disc spot).

Fig. 10
Fig. 10

(a) Randomly generated beamlet intensities for a uniformity of 30% (U = 0.3) and a zeroth-order diffraction ratio of I 0 = 1. (b) Computed exit-pupil pattern obtained by the convolution of the beam profile at the aperture by the beamlet intensities shown in (a).

Fig. 11
Fig. 11

Exit-pupil uniformity as perceived by the viewer for (a) a 2-mm and (b) a 5-mm eye-pupil size as obtained by use of the computed exit-pupil pattern of Fig. 10(b).

Fig. 12
Fig. 12

System exit-pupil uniformity plotted as a function of the s/ d ratio and T. It is assumed that P ep = 15 mm, there is a 13 × 13 array of beamlets, U = 0.3, I 0 = 1, and the eye-pupil size is 2 mm. The crosses show to which contour line the contour labels belong.

Fig. 13
Fig. 13

PSF measurements obtained by use of the EPE of Fig. 2(b) that has a cell period of 16 µm. The spot in the EPE is imaged onto a CCD by use of a microscope objective and an aperture that mimic a 2-mm eye pupil. Top row, left-most image: the PSF without an EPE. Remaining images: same measurement with the EPE in place and obtained by the movement of the EPE horizontally relative to the focused spot in 2-µm steps.

Fig. 14
Fig. 14

Results of the repetition of the experiment of Fig. 13 but with an aperture that mimics a 5-mm eye pupil.

Fig. 15
Fig. 15

Horizontal component of the MTF for the PSFs shown in (a) Fig. 13 (2-mm eye-pupil case) and (b) Fig. 14 (5-mm eye-pupil case). The vertical MTF remains constant when the grating is moved horizontally relative to the spot. The curve that represents no use of the EPE is marked with open circles. The other curves each correspond to a different spot position across the EPE. (a) Eight and (b) 16 different spot positions were used to compute the MTFs.

Fig. 16
Fig. 16

Extremum values of the horizontal (Hor.) and the vertical (Ver.) MTFs at the display cutoff frequency plotted as a function of the eye-pupil size. The variation of the MTF is obtained by the movement of the EPE diagonally relative to the focused static spot.

Equations (17)

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

Pep tanθFOV/2=D tanθTOSA/2.
D tanθTOSA/2=L tanθi,  L tanθ0=Pep tanθFOV/2.
U=IMax-IMinIMax+IMin 100.
Uoutx, y=Uinx, yexpjϕx, y,
Sk, m=0d0d expjϕx, y×exp-j2πkxd+myddxdy,
ϕx, y=ϕ0x, yA10x, yA0,
η=k,mW |Sk, m|2.
sin θkm cos ϕkm=sin θinc+kλ/d,  sin θkm sin ϕkm=mλ/d,
ϕ0n, λ, t, θinc=2πtλncossin-1sin θinc/n-1cos θinc,
tπ=λ2n-1.
I0=|S0, 0|2=0d0d expjϕx, ydxdy2,
I0=|A0+A1 expjϕ0|2=A02+A12+2A0A1 cos ϕ0.
ϕ0=π1+εn-1ncossin-1sin θinc/n-1cos θinc.
Iavg=ηNepe,
s=KTλf#,
T=2wm/D,
KT=1.036-0.058/T+0.156/T2if T0.40.75/Tif T0.4.

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