Abstract

The information contained in a complete interferogram and in a spectra are equivalent, but within a portion of an interferogram the two contain different information and cannot be directly compared. The partial interferogram provides information about particular types of structure within the spectra and may be better suited to a particular task than the spectra which contains much information of no value to the particular task. The advantages of partially scanned interferograms for remote soundings of atmospheric temperature are discussed, and several examples are given. These suggest that partially scanned interferograms can provide more detailed and versatile information than the presently used techniques. In particular, they seem able to cope with the temperatures near the ground and temperature inversions.

© 1977 Optical Society of America

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References

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  1. J. T. Houghton, S. D. Smith, Proc. R. Soc. London Ser. A 320, 23 (1970).
    [Crossref]
  2. G. A. Vanasse, H. Sakai, in Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1967), Vol. 6, pp. 259–330.
    [Crossref]
  3. R. Dick, G. Levy, in Aspen International Conference on Fourier Spectroscopy; AFCRL Special Report 114 (1970), pp. 353–360.
  4. D. Q. Wark, H. E. Fleming, Mon. Weather Rev. 94, 351 (1966).
    [Crossref]
  5. T. G. Kyle, J. Quant. Spectrosc. Radiat. Transfer 9, 1477 (1969).
    [Crossref]
  6. R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRL Environmental Research Papers 434 (1973).
  7. S. L. Valley, Ed., Handbook of Geophysics and Space Environments, AFCRL, Cambridge, Mass. (1965), pp. 2–13.
  8. S. Twomey, Mon. Weather Rev. 94, 363 (1966).
    [Crossref]
  9. E. R. Huppi, J. W. Rogers, A. T. Stair, Appl. Opt. 13, 1466 (1974).
    [Crossref] [PubMed]
  10. F. W. Taylor, Appl. Opt. 13, 1559 (1974).
    [Crossref] [PubMed]

1974 (2)

1970 (1)

J. T. Houghton, S. D. Smith, Proc. R. Soc. London Ser. A 320, 23 (1970).
[Crossref]

1969 (1)

T. G. Kyle, J. Quant. Spectrosc. Radiat. Transfer 9, 1477 (1969).
[Crossref]

1966 (2)

S. Twomey, Mon. Weather Rev. 94, 363 (1966).
[Crossref]

D. Q. Wark, H. E. Fleming, Mon. Weather Rev. 94, 351 (1966).
[Crossref]

Benedict, W. S.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRL Environmental Research Papers 434 (1973).

Burch, D. E.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRL Environmental Research Papers 434 (1973).

Calfee, R. F.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRL Environmental Research Papers 434 (1973).

Clough, S. A.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRL Environmental Research Papers 434 (1973).

Dick, R.

R. Dick, G. Levy, in Aspen International Conference on Fourier Spectroscopy; AFCRL Special Report 114 (1970), pp. 353–360.

Fleming, H. E.

D. Q. Wark, H. E. Fleming, Mon. Weather Rev. 94, 351 (1966).
[Crossref]

Fox, K.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRL Environmental Research Papers 434 (1973).

Garing, J. S.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRL Environmental Research Papers 434 (1973).

Houghton, J. T.

J. T. Houghton, S. D. Smith, Proc. R. Soc. London Ser. A 320, 23 (1970).
[Crossref]

Huppi, E. R.

Kyle, T. G.

T. G. Kyle, J. Quant. Spectrosc. Radiat. Transfer 9, 1477 (1969).
[Crossref]

Levy, G.

R. Dick, G. Levy, in Aspen International Conference on Fourier Spectroscopy; AFCRL Special Report 114 (1970), pp. 353–360.

McClatchey, R. A.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRL Environmental Research Papers 434 (1973).

Rogers, J. W.

Rothman, L. S.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRL Environmental Research Papers 434 (1973).

Sakai, H.

G. A. Vanasse, H. Sakai, in Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1967), Vol. 6, pp. 259–330.
[Crossref]

Smith, S. D.

J. T. Houghton, S. D. Smith, Proc. R. Soc. London Ser. A 320, 23 (1970).
[Crossref]

Stair, A. T.

Taylor, F. W.

Twomey, S.

S. Twomey, Mon. Weather Rev. 94, 363 (1966).
[Crossref]

Vanasse, G. A.

G. A. Vanasse, H. Sakai, in Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1967), Vol. 6, pp. 259–330.
[Crossref]

Wark, D. Q.

D. Q. Wark, H. E. Fleming, Mon. Weather Rev. 94, 351 (1966).
[Crossref]

Appl. Opt. (2)

J. Quant. Spectrosc. Radiat. Transfer (1)

T. G. Kyle, J. Quant. Spectrosc. Radiat. Transfer 9, 1477 (1969).
[Crossref]

Mon. Weather Rev. (2)

D. Q. Wark, H. E. Fleming, Mon. Weather Rev. 94, 351 (1966).
[Crossref]

S. Twomey, Mon. Weather Rev. 94, 363 (1966).
[Crossref]

Proc. R. Soc. London Ser. A (1)

J. T. Houghton, S. D. Smith, Proc. R. Soc. London Ser. A 320, 23 (1970).
[Crossref]

Other (4)

G. A. Vanasse, H. Sakai, in Progress in Optics, E. Wolf, Ed. (North-Holland, Amsterdam, 1967), Vol. 6, pp. 259–330.
[Crossref]

R. Dick, G. Levy, in Aspen International Conference on Fourier Spectroscopy; AFCRL Special Report 114 (1970), pp. 353–360.

R. A. McClatchey, W. S. Benedict, S. A. Clough, D. E. Burch, R. F. Calfee, K. Fox, L. S. Rothman, J. S. Garing, AFCRL Environmental Research Papers 434 (1973).

S. L. Valley, Ed., Handbook of Geophysics and Space Environments, AFCRL, Cambridge, Mass. (1965), pp. 2–13.

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Figures (7)

Fig. 1
Fig. 1

The resolution function resulting from a partially scanned interferogram is shown. In this case all elements of the interferogram except those between 1.68 cm and 2.05 cm were taken to be zero. The nonzero elements were taken to be unity, If all values less than 2.05 cm had been unity, the result would have been a sinc function.

Fig. 2
Fig. 2

The transmittances of the atmosphere above altitudes 0, 4, 8, 12, 16, 20, 24, and 30 km are shown. The primary absorber is CO2, but some water absorption lines can be seen for wavenumbers greater than 740 cm−1. There is an offset of 30% between each altitude. The altitudes increase from the bottom to the top of the figure.

Fig. 3
Fig. 3

The radiance reaching the top of the atmosphere from a constant temperature slab is proportional to the difference of the transmittances from the top and bottom to the top of the atmosphere. The differences obtained by subtracting the 0–4, 4–8, 8–12, 12–16, 16–20, 20–24, and 24–30 km are shown. The 0–4-km curve is at the bottom of the figure, with successive offsets of 30% for the next higher layer. The layers used in the remainder of the paper were not so thick as these.

Fig. 4
Fig. 4

The interferograms which would be obtained if only individual layers of the atmosphere could be observed are shown. These assume the atmosphere above the particular layer still attenuate the emission of the layer, but does not contribute to the emission. That is, if the differences of transmittance shown in Fig. 3 are multiplied by the appropriate blackbody function, the absolute value of the transform is the quantity shown above. In this figure the higher layers are displaced downward, so the curves from top to bottom represent the observed emission of the ground layers between 0–4, 4–8, 8–12, 12–16, 16–20, 20–24, 24–30, and the atmosphere above 30 km, respectively.

Fig. 5
Fig. 5

The temperature of the ground is shown at altitude 0 km, with the first layer temperature at altitude 0.4 km, the second layer temperature at altitude 2 km, etc. The input temperature is the solid curve, and the deduced temperature is the broken curve. In this case the ground is colder than the lowest layer of the atmosphere, and there is a temperature inversion due to the lowest layer.

Fig. 6
Fig. 6

The solid curve is the input temperature, and the broken curve is the deduced temperature. Again, the ground is colder than the lowest layer of the atmosphere, but now the temperature inversion is at a higher altitude.

Fig. 7
Fig. 7

It is difficult to see the difference in the input and the deduced temperature in this figure. The change of the temperature was 4 K from the standard case for a 4-km thick layer.

Tables (1)

Tables Icon

Table I Temperatures TI are Changes from the Given Standard Case Temperature

Equations (30)

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2 σ X = N
f ( σ ) = sin ( 2 π σ X 2 ) 2 π σ X 2 = sinc ( 2 σ X 2 ) .
f ( σ ) = sinc ( 2 σ X 2 ) - sinc ( 2 σ X 1 ) .
S ( σ ) = - f ( σ + x ) S T ( x ) d x .
S ˜ ( x ) = 0 S ( σ ) cos ( 2 π σ x ) d σ .
S T ( σ ) = B 1 ( σ 1 , θ 1 ) T 1 ( σ ) + j = 2 K B j ( σ , θ j ) [ T j ( σ ) - T j - 1 ( σ ) ] ,
I i = I i + j Δ Q j I Q j + j ( Δ Q j ) 2 2 I i Q j ,
j W i j I i Q k = { 0 j k , 1 j = k ,
i W i j 2 = minimum .
i ( I i - I i ) W i j = Q j .
N j = [ j ( W i j N ) 2 ] = N 2 ( i W i j 2 ) .
I i ( Q j ) = I i ( Q j ) + j ( Q j - Q j ) I i ( Q j ) Q j + j ( Q j - Q j ) 2 2 I i ( Q j ) Q j 2 .
D i k = ( I i ) / ( Q k ) ,
q k = Q k - Q k ;
D i k = ( 2 I i ) / ( Q k - J 2 ) ,
q k = ( Q k - J - Q k - J ) 2 .
i W i k [ I i ( Q ) - I i ( Q ) ] = i n W i k Q n D i n = Q k ,
k W i k D k j = δ i j
i W i j 2 = C j = minimum .
N k 2 = i W i k N i 2 = N 2 i W i k 2 .
N k = ( N 2 / M ) 1 / 2 .
j W i j 2 - i k B i k W i k D k j = V j
i ( W i j 2 - k B i k W i k D k j ) = V j .
V j W i j = 0 = i ( 2 W i j - k B i k D k j )
W i k = 1 2 k B i n D n k .
n B i n k D n k D k j = δ i j .
k D n k D k j
n B i n A n j = δ i j
B i n = j δ i j A j n - 1 = A i n - 1 .
W i k = 1 2 n A i n - 1 D n k .

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