Abstract

Sensitivity often restricts remote Raman spectrometers to operate at ranges inside their very large hyperfocal distances. Operation against a daylit background then requires minimizing the system etendue. This can be done by focusing the system at the range of interest; the depth of field is then etendue limited and varies with the square of the range. For the usual case of depth of field limited sampling depth, this cancels the inverse square range effect on signal strength, making the signal range independent (if atmospheric absorption is neglected). This concept is proven analytically and experimentally.

© 1974 Optical Society of America

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References

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  1. T. Hirschfeld, E. R. Schildkraut, H. Tannenbaum, D. Tanenbaum, Appl. Phys. Lett. 22, 38 (1973).
    [CrossRef]
  2. T. Hirschfeld, S. Klainer, R. Burton, in Proc. Electrooptical Systems Design Symp., K. A. Kopetsky, Ed. (Industrial and Scientific Conference Management, Chicago, Ill., 1970), p. 418–27.
  3. P. Jacquinot, J. Opt. Soc. Am. 44, 761 (1954).
    [CrossRef]
  4. Z. Zachor, “Throughput—A Figure of Merit for Optical Systems,” Advertisement, J. Opt. Soc. Am. 54, No. 1 (1964).

1973 (1)

T. Hirschfeld, E. R. Schildkraut, H. Tannenbaum, D. Tanenbaum, Appl. Phys. Lett. 22, 38 (1973).
[CrossRef]

1964 (1)

Z. Zachor, “Throughput—A Figure of Merit for Optical Systems,” Advertisement, J. Opt. Soc. Am. 54, No. 1 (1964).

1954 (1)

Burton, R.

T. Hirschfeld, S. Klainer, R. Burton, in Proc. Electrooptical Systems Design Symp., K. A. Kopetsky, Ed. (Industrial and Scientific Conference Management, Chicago, Ill., 1970), p. 418–27.

Hirschfeld, T.

T. Hirschfeld, E. R. Schildkraut, H. Tannenbaum, D. Tanenbaum, Appl. Phys. Lett. 22, 38 (1973).
[CrossRef]

T. Hirschfeld, S. Klainer, R. Burton, in Proc. Electrooptical Systems Design Symp., K. A. Kopetsky, Ed. (Industrial and Scientific Conference Management, Chicago, Ill., 1970), p. 418–27.

Jacquinot, P.

Klainer, S.

T. Hirschfeld, S. Klainer, R. Burton, in Proc. Electrooptical Systems Design Symp., K. A. Kopetsky, Ed. (Industrial and Scientific Conference Management, Chicago, Ill., 1970), p. 418–27.

Schildkraut, E. R.

T. Hirschfeld, E. R. Schildkraut, H. Tannenbaum, D. Tanenbaum, Appl. Phys. Lett. 22, 38 (1973).
[CrossRef]

Tanenbaum, D.

T. Hirschfeld, E. R. Schildkraut, H. Tannenbaum, D. Tanenbaum, Appl. Phys. Lett. 22, 38 (1973).
[CrossRef]

Tannenbaum, H.

T. Hirschfeld, E. R. Schildkraut, H. Tannenbaum, D. Tanenbaum, Appl. Phys. Lett. 22, 38 (1973).
[CrossRef]

Zachor, Z.

Z. Zachor, “Throughput—A Figure of Merit for Optical Systems,” Advertisement, J. Opt. Soc. Am. 54, No. 1 (1964).

Advertisement, J. Opt. Soc. Am. (1)

Z. Zachor, “Throughput—A Figure of Merit for Optical Systems,” Advertisement, J. Opt. Soc. Am. 54, No. 1 (1964).

Appl. Phys. Lett. (1)

T. Hirschfeld, E. R. Schildkraut, H. Tannenbaum, D. Tanenbaum, Appl. Phys. Lett. 22, 38 (1973).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (1)

T. Hirschfeld, S. Klainer, R. Burton, in Proc. Electrooptical Systems Design Symp., K. A. Kopetsky, Ed. (Industrial and Scientific Conference Management, Chicago, Ill., 1970), p. 418–27.

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Figures (3)

Fig. 1
Fig. 1

Geometry of remote Raman illumination and collection.

Fig. 2
Fig. 2

Perifocal region of remote Raman illumination and collection.

Fig. 3
Fig. 3

Focal ratio dependence of atmospheric nitrogen Raman return.

Equations (22)

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L e = - Δ Z / 2 + Δ Z / 2 E Z d Z ,
d Z = ( d I 2 + Z 2 θ I 2 ) 1 / 2
d Z = ( d C 2 + Z 2 θ C 2 ) , 1 / 2
d C = d L ( θ a / θ C ) 2.44 ( λ / θ C ) ,
d I = d 0 ( θ 0 / θ I ) ( 2 / π ) ( λ / θ I ) ,
d s = f M θ C ( d Z 2 + d Z 2 ) 1 / 2 = f M θ C × [ ( d 0 2 θ 0 2 / θ I 2 ) + ( d L 2 θ a 2 / θ C 2 ) + Z 2 ( θ C 2 + θ I 2 ) ] 1 / 2 ,
( E Z ) d s d A 1 ;             ( E Z ) d s > d A = ( d A / d s ) 2 ,
( L e ) d s d A = Δ Z
( L e ) d s > d A = d A 2 f M 2 θ c 2 - Δ Z / 2 + Δ Z / 2 d Z d 0 2 θ 2 / θ I 2 + d L 2 θ a 2 / θ c 2 + Z 2 ( θ c 2 + θ I 2 ) = d A 2 f M 2 θ c 2 × { arctan x [ ( θ I 2 + θ c 2 ) / ( d 0 2 θ 0 2 / θ I 2 + d L 2 θ a 2 / θ L 2 ) ] 1 / 2 [ ( θ c 2 + θ I 2 ) ( d 0 2 θ 0 2 / θ I 2 + d L 2 θ a 2 / θ c 2 ) ] - Δ Z / 2 1 / 2 } - Δ Z / 2 + Δ Z / 2
( L e ) d s > d A , = d A 2 f M 2 θ c 2 - + d Z d 0 2 θ 0 2 / θ I 2 + d L 2 θ a 2 / θ c 2 + Z 2 ( θ c 2 + θ I 2 ) = π d A 2 f M 2 θ c 2 [ ( θ c 2 + θ I 2 ) ( d 0 2 / θ I 2 + d L 2 θ a 2 / θ c 2 ) ] 1 / 2 .
( L e ) d s < d A , d Z > > d Z = d A 2 f M 2 θ c 2 d L θ a [ arctan ( x θ c 2 d L θ a ) ] - Δ Z / 2 + Δ Z / 2 ,
( L e ) d s < d A , d Z < < d Z = d A 2 f M 2 θ I 2 d 0 θ 0 [ arctan ( x θ I 2 d 0 θ 0 ) ] - Δ Z / 2 + Δ Z / 2 ,
θ C = d L / R ; θ I = d 0 / R ,
M = θ c 2 / 16.
S α M L e ,
( L e ) d s > d A = π d A 2 R 2 f M 2 d L 2 [ ( d L 2 + d 0 2 ) ( θ 0 2 + θ a 2 ) ] 1 / 2 ,
S α π d A 2 16 f M 2 [ ( d L 2 + d 0 2 ) ( θ 0 2 + θ a 2 ) ] 1 / 2 .
τ a = ( π 2 / 16 ) ( d A 2 / f M 2 )
τ a = ( π 2 / 16 ) ( d L 2 + d 0 2 ) ( θ 0 2 + θ a 2 ) .
S α [ 4 τ a / ( τ a ) 1 / 2 ] ,
S / N α 4 ( τ a / τ a ) 1 / 2 .
S α ( τ a / π d L θ 0 ) .

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