Abstract

An ir field optics system has been designed that achieves the maximum flux concentration allowed by the Abbe sine inequality and provides efficient coupling to bolometer-type detectors.

© 1976 Optical Society of America

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References

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  1. Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
    [CrossRef]
  2. M. J. Rudd, J. Phys. E 2, 55 (1969).
    [CrossRef]
  3. F. Durst, J. Appl. Math. & Phys. (ZAMP) 24, 619 (1973).
  4. G. Oster, Y. Nishijima, Sci. Am. 208, 54 (1963).
    [CrossRef]
  5. J. Guild, The Interference Systems of Crossed Diffraction Gratings: Theory of Moiré Fringes (Oxford U. P., New York, 1956).
  6. H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1956).
  7. R. J. Goldstein, D. K. Kreid, J. Appl. Mech. 34, 813 (1967).
    [CrossRef]
  8. F. Durst, J. H. Whitelaw, Proc. R. Soc. Lond. A324, 157 (1971).
  9. S. Hanson, J. Phys. D 6, 164 (1973).
    [CrossRef]
  10. W. J. Hiller, G. E. A. Meier, Dimensionierung und Jus-tierung von Laseranemometern bei der Verwendung von Wol-laston-Prismen als Strahlteiler, Max-Planck-Institut fur Strömungsforschung, Bericht 12/1973, Göttingen (1973).

1973 (2)

F. Durst, J. Appl. Math. & Phys. (ZAMP) 24, 619 (1973).

S. Hanson, J. Phys. D 6, 164 (1973).
[CrossRef]

1971 (1)

F. Durst, J. H. Whitelaw, Proc. R. Soc. Lond. A324, 157 (1971).

1969 (1)

M. J. Rudd, J. Phys. E 2, 55 (1969).
[CrossRef]

1967 (1)

R. J. Goldstein, D. K. Kreid, J. Appl. Mech. 34, 813 (1967).
[CrossRef]

1964 (1)

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

1963 (1)

G. Oster, Y. Nishijima, Sci. Am. 208, 54 (1963).
[CrossRef]

1956 (1)

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1956).

Cummins, H. Z.

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

Durst, F.

F. Durst, J. Appl. Math. & Phys. (ZAMP) 24, 619 (1973).

F. Durst, J. H. Whitelaw, Proc. R. Soc. Lond. A324, 157 (1971).

Goldstein, R. J.

R. J. Goldstein, D. K. Kreid, J. Appl. Mech. 34, 813 (1967).
[CrossRef]

Guild, J.

J. Guild, The Interference Systems of Crossed Diffraction Gratings: Theory of Moiré Fringes (Oxford U. P., New York, 1956).

Hanson, S.

S. Hanson, J. Phys. D 6, 164 (1973).
[CrossRef]

Hiller, W. J.

W. J. Hiller, G. E. A. Meier, Dimensionierung und Jus-tierung von Laseranemometern bei der Verwendung von Wol-laston-Prismen als Strahlteiler, Max-Planck-Institut fur Strömungsforschung, Bericht 12/1973, Göttingen (1973).

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1956).

Kreid, D. K.

R. J. Goldstein, D. K. Kreid, J. Appl. Mech. 34, 813 (1967).
[CrossRef]

Meier, G. E. A.

W. J. Hiller, G. E. A. Meier, Dimensionierung und Jus-tierung von Laseranemometern bei der Verwendung von Wol-laston-Prismen als Strahlteiler, Max-Planck-Institut fur Strömungsforschung, Bericht 12/1973, Göttingen (1973).

Nishijima, Y.

G. Oster, Y. Nishijima, Sci. Am. 208, 54 (1963).
[CrossRef]

Oster, G.

G. Oster, Y. Nishijima, Sci. Am. 208, 54 (1963).
[CrossRef]

Rudd, M. J.

M. J. Rudd, J. Phys. E 2, 55 (1969).
[CrossRef]

Whitelaw, J. H.

F. Durst, J. H. Whitelaw, Proc. R. Soc. Lond. A324, 157 (1971).

Yeh, Y.

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1956).

J. Appl. Math. & Phys. (ZAMP) (1)

F. Durst, J. Appl. Math. & Phys. (ZAMP) 24, 619 (1973).

J. Appl. Mech. (1)

R. J. Goldstein, D. K. Kreid, J. Appl. Mech. 34, 813 (1967).
[CrossRef]

J. Phys. D (1)

S. Hanson, J. Phys. D 6, 164 (1973).
[CrossRef]

J. Phys. E (1)

M. J. Rudd, J. Phys. E 2, 55 (1969).
[CrossRef]

Proc. R. Soc. Lond. (1)

F. Durst, J. H. Whitelaw, Proc. R. Soc. Lond. A324, 157 (1971).

Sci. Am. (1)

G. Oster, Y. Nishijima, Sci. Am. 208, 54 (1963).
[CrossRef]

Other (2)

J. Guild, The Interference Systems of Crossed Diffraction Gratings: Theory of Moiré Fringes (Oxford U. P., New York, 1956).

W. J. Hiller, G. E. A. Meier, Dimensionierung und Jus-tierung von Laseranemometern bei der Verwendung von Wol-laston-Prismen als Strahlteiler, Max-Planck-Institut fur Strömungsforschung, Bericht 12/1973, Göttingen (1973).

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Figures (9)

Fig. 1
Fig. 1

Heat trap (schematic). The parabola P (axis A and focus F) is rotated about the optic axis Z to generate the collector surface. The surface is parallel to Z at the entrance aperture. The angle θ1 between A and Z is equal to the cutoff angle for entering rays. The collector is drawn for θ1 = 10° corresponding to a telescope focal ratio fT = 2.88.

Fig. 2
Fig. 2

Idealized configurations of field optics systems employing concave mirrors and on-axis detectors: (A) disk-shaped detector; (B) spherical detector. In each case θ1 = θT.

Fig. 3
Fig. 3

Angular cutoff interval of an ideal light collector calculated for a point source at infinity with λ ≪ d2. The quantity Δθ is the angular interval in which the intensity drops from ¾ to ¼ of its maximum value (see inset).

Fig. 4
Fig. 4

Observed (solid line) and calculated (dashed line) ir beam patterns for three heat traps with cylindrical cavities (Table I). The calculated curves take into account the inherent acceptance of the collectors (Fig. 4), diffraction at the entrance apertures, losses at each reflection, and the finite apertures of the test source and collectors. The arrows indicate the nominal cutoff angles θ1.

Fig. 5
Fig. 5

Observed ir beam pattern for a 7.2° heat trap with a hemispherical cavity (see inset Fig. 7).

Fig. 6
Fig. 6

Optical model (schematic). The entrance aperture of the model heat trap is exposed to uniform illumination from the inside surfaces of the white box. The light reflected at angle θ is measured by the photocell.

Fig. 7
Fig. 7

Beam patterns obtained with the optical model (reflected light). The bottom curve was obtained with the exit aperture of the light collector opening into a dark room. The top curve was obtained with a hemispherical cavity (inset) of proportions dB = 1.2d2 and rC = 3.3d2 with the bolometer surface below the aperture by d2/2. The solid-line curves were obtained with a gray bolometer in a cylindrical cavity of proportions dB = d2 and dC = lC = 2dB at various values of lB/lC (symbols defined in Fig. 1).

Fig. 8
Fig. 8

Beam patterns of a 2.2° heat trap of exit diameter d2 = 330 μm at wavelengths λ = 280 μm (solid line) and λ = 550 μm (dashed line). [The solid angle of the source was larger than that used for Fig. 4(A).]

Fig. 9
Fig. 9

Scan of Jupiter at the 5-m Hale telescope using the 7.2° heat trap. The calculated field of view (diameter 3.05-min of arc) is indicated by the arrows. The lower portion of the figure shows, for comparison, the convolution of a 3.05-min of arc aperture with the diffraction pattern expected for a point source at a wavelength λ = 1.4 mm.

Tables (2)

Tables Icon

Table I Dimensions of Heat Traps Used in Performance Tests

Tables Icon

Table II Signals from Sources Observed at the 5-m Hale Telescope Using the 7.2° Heat Trap

Equations (28)

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C = S 1 / S 2 ,
r 2 / r 1 = f F / f T ,
f T = 1 / ( 2 sin θ T ) .
C = 1 / ( 2 f F sin θ T ) 2 .
C ( lens ) 1 / ( 4 sin 2 θ T ) .
d 1 = 2 r sin ϕ
d 2 = 2 r sin 2 θ T ,
d 2 / d 1 = sin 2 θ T / sin ϕ .
C ( mirror , disk detector ) = ( d 1 / d 2 ) 2 1 = [ 1 / ( 4 sin 2 θ T ) ] ( cos 2 θ T / cos θ T ) 2 < 1 / ( 4 sin 2 θ T ) ,
S 1 / S 2 = d 1 2 / 4 d 2 2 ,
C ( mirror , spherical detector ) 1 / 4 sin 2 θ T ) ,
r 2 = r 1 sin θ 1 .
C ( i deal light collector ) = 1 / sin 2 θ T .
δ = 1.22 λ f T .
r 2 1.22 λ f F .
K λ f F r 2 1.22 λ f F
θ 1 = arcsin ( 1 / 2 f T ) .
r 1 = θ b f T d T ,
d 2 = d 1 sin θ 1 ;
d 2 = d 1 / 2 f T ,
l L = ( d 1 + d 2 ) / ( 2 tan θ 1 ) ;
l L = d 2 ( 2 f T + 1 ) ( 4 f T 2 1 ) 1 / 2 / 2 ,
d B d 2 ,
d C 2 d B ,
l C d C ,
l B 0.35 l C .
I / I 0 = abc ( r 1 / r 2 ) 2 .
K λ d 2 1.22 λ .

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