Abstract

The properties of simple and multiple Fabry–Perot-type interference filters with aluminum films as the reflecting layers are deduced with the aid of the measured optical constants of aluminum. Computed transmission curves are given for several filters of these types in the wavelength range from 1500 to 2500 Å. The properties of multiple-stack filters, two or more simple three-layer interference filters stacked contiguously, are deduced. It is shown that multiple-stack filters have definite advantages over three-layer interference filters. In particular, improvement in contrast without significant increase in bandwidth is obtained. Combination of a first- and second-order filter in the same multiple-stack filter is shown to give a reduced bandwidth, as expected. Experimental results for multiple filters confirm the predicted theoretical advantages.

© 1962 Optical Society of America

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References

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  1. Space Astronomy Laboratory, University of Wisconsin, OAO Experiment Description Outline (February1961).
  2. J. E. Kupperian and R. R. Zeimer, Intern. Sci. and Tech. (March, 1962).
  3. H. B. Hallock, Appl. Optics 1, 155 (1962).
    [CrossRef]
  4. G. Hass and J. E. Waylonis, J. Opt. Soc. Am. 51, 719 (1961).
    [CrossRef]
  5. P. H. Berning, G. Hass, and R. P. Madden, J. Opt. Soc. Am. 50, 586 (1960).
    [CrossRef]
  6. G. Koppelmann and K. Krebs, Z. Physik 156, 38 (1959).
    [CrossRef]
  7. G. Honcia and K. Krebs, Z. Physik 156, 117 (1959).
    [CrossRef]
  8. G. Honcia, dissertation, Technical University of Berlin, 1960.
  9. J. A. Berning and P. H. Berning, J. Opt. Soc. Am. 50, 813 (1960).
    [CrossRef]
  10. O. S. Heavens, Optical Properties of Thin Solid Films, (Butterworth Scientific Publications, Ltd., London, 1955), Chap. 7.
  11. G. Hass, W. R. Hunter, and R. Tousey, J. Opt. Soc. Am. 46, 1009 (1956); J. Opt. Soc. Am. 47, 1070 (1957).
    [CrossRef]
  12. Below 1500 Å the constants of freshly evaporated aluminum (a few seconds old) are somewhat different than those given in Fig. 2. However, oxidation within the film rapidly changes the characteristics until a “steady-state” condition is reached where the optical constants are approximately those given in Fig. 2. The constants for this “steady-state” are used for deducing the aluminum-film properties.

1962 (2)

J. E. Kupperian and R. R. Zeimer, Intern. Sci. and Tech. (March, 1962).

H. B. Hallock, Appl. Optics 1, 155 (1962).
[CrossRef]

1961 (2)

Space Astronomy Laboratory, University of Wisconsin, OAO Experiment Description Outline (February1961).

G. Hass and J. E. Waylonis, J. Opt. Soc. Am. 51, 719 (1961).
[CrossRef]

1960 (2)

1959 (2)

G. Koppelmann and K. Krebs, Z. Physik 156, 38 (1959).
[CrossRef]

G. Honcia and K. Krebs, Z. Physik 156, 117 (1959).
[CrossRef]

1956 (1)

Berning, J. A.

Berning, P. H.

Hallock, H. B.

H. B. Hallock, Appl. Optics 1, 155 (1962).
[CrossRef]

Hass, G.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films, (Butterworth Scientific Publications, Ltd., London, 1955), Chap. 7.

Honcia, G.

G. Honcia and K. Krebs, Z. Physik 156, 117 (1959).
[CrossRef]

G. Honcia, dissertation, Technical University of Berlin, 1960.

Hunter, W. R.

Koppelmann, G.

G. Koppelmann and K. Krebs, Z. Physik 156, 38 (1959).
[CrossRef]

Krebs, K.

G. Koppelmann and K. Krebs, Z. Physik 156, 38 (1959).
[CrossRef]

G. Honcia and K. Krebs, Z. Physik 156, 117 (1959).
[CrossRef]

Kupperian, J. E.

J. E. Kupperian and R. R. Zeimer, Intern. Sci. and Tech. (March, 1962).

Madden, R. P.

Tousey, R.

Waylonis, J. E.

Zeimer, R. R.

J. E. Kupperian and R. R. Zeimer, Intern. Sci. and Tech. (March, 1962).

Appl. Optics (1)

H. B. Hallock, Appl. Optics 1, 155 (1962).
[CrossRef]

Intern. Sci. and Tech. (1)

J. E. Kupperian and R. R. Zeimer, Intern. Sci. and Tech. (March, 1962).

J. Opt. Soc. Am. (4)

OAO Experiment Description Outline (1)

Space Astronomy Laboratory, University of Wisconsin, OAO Experiment Description Outline (February1961).

Z. Physik (2)

G. Koppelmann and K. Krebs, Z. Physik 156, 38 (1959).
[CrossRef]

G. Honcia and K. Krebs, Z. Physik 156, 117 (1959).
[CrossRef]

Other (3)

G. Honcia, dissertation, Technical University of Berlin, 1960.

O. S. Heavens, Optical Properties of Thin Solid Films, (Butterworth Scientific Publications, Ltd., London, 1955), Chap. 7.

Below 1500 Å the constants of freshly evaporated aluminum (a few seconds old) are somewhat different than those given in Fig. 2. However, oxidation within the film rapidly changes the characteristics until a “steady-state” condition is reached where the optical constants are approximately those given in Fig. 2. The constants for this “steady-state” are used for deducing the aluminum-film properties.

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of a multiple-stack filter made up of two simple three-layer interference filters.

Fig. 2
Fig. 2

The refractive indices and absorption constants for those materials most frequently used for filters in the ultraviolet. These curves were obtained by fitting three constant Cauchy equations, Eqs. (1) and (2), to the measured optical constants.

Fig. 3
Fig. 3

Computed reflectance (full line) and transmittance (dashed line) curves for several thicknesses of aluminum as a function of wavelength. These results are obtained with theoretical constants of aluminum shown in Fig. 2. The substrate is assumed to be transparent with an index of 1.50.

Fig. 4
Fig. 4

Computed absorptance of several thicknesses of aluminum as a function of wavelength. The index on both sides of the aluminum film is assumed to be 1.00.

Fig. 5
Fig. 5

Computed bandwidth and finesse of a three-layer interference filter as a function of the wavelength of peak transmission. The thicknesses of the semitransparent aluminum films are such that the peak transmittance of a given filter is 25%.

Fig. 6
Fig. 6

Computed phase shift at an aluminum–magnesium fluoride boundary for two different aluminum-film thicknesses. For λ>1500 Å the phase change for opaque aluminum films is essentially the same as for a 250-Å film.

Fig. 7
Fig. 7

Computed transmission curves for a 3MDM and 5MDM filter, each peaked at 2500 Å. Each of the aluminum films in the 3MDM filter is 200 Å thick. The outer aluminum films in the 5MDM filter are each 140 Å thick; the center film is 300 Å thick. The substrate is transparent with an index of 1.50.

Fig. 8
Fig. 8

Computed transmission curves of three 5MDM multiple stack filters with transmission peaks at 1500, 1800, and 2200 Å. The 1500- and 2200 Å filters are first order at these wavelengths; the 1800 Å filter is a combined first- and second-order filter. The outer aluminum films in the 1500-, 1800-, and 2200-Å filters are 150, 160, and 140 Å thick, respectively; the center aluminum film is 300, 320, and 300 Å thick, respectively.

Fig. 9
Fig. 9

Transmission curves of Fig. 8 presented on a linear scale.

Fig. 10
Fig. 10

Experimental transmission curves of one 3MDM filter and two 5MDM filters.

Fig. 11
Fig. 11

Experimental transmission curves of two 5MDM filters.

Equations (7)

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n j = B 1 j + B 2 j λ - 2 + B 3 j λ - 4 ,
k j = C 1 j + C 2 j λ - 2 + C 3 j λ - 4 ,
peak transmittance = 1 / [ 1 + ( A / T ) ] 2 ,
bandwidth = [ ( 1 - R ) / π R 1 2 ] λ ,
n 1 t = ( λ / 2 π ) ( m π - α ) ;             m = 1 , 2 , ,
tan α = 2 n 1 k / ( n 2 + k 2 - n 1 2 ) ,
contrast = [ ( 1 + R ) / ( 1 - R ) ] 2 .