Abstract

A bandpass filter of the double-halfwave design has been developed for use in submillimeter astronomy. The filter is rugged, easily tunable, easy to construct, and cryogenically coolable without loss of performance. Its bandpass character is superior to the single Fabry-Perot.

© 1984 Optical Society of America

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References

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  1. R. Ulrich, K. F. Renk, L. Genzel, “Tunable Submillimeter Interferometers of the Fabry-Perot Type,” IEEE Trans. Microwave Theory Tech. MTT-11, 363 (1963).
    [CrossRef]
  2. G. D. Holah, B. Davis, N. D. Morrison, “Narrow-Bandpass Filters for the Far-Infrared using Double-Half-Wave Designs,” Infrared Phys. 19, 639 (1979).
    [CrossRef]
  3. At mountain altitudes (4.2 km) the atmosphere is ~30% transparent in these bands; see W. A. Traub, M. T. Stier, “Theoretical Atmospheric Transmission in the Mid- and Far-Infrared at Four Altitudes,” Appl. Opt. 15, 364 (1976).
    [CrossRef] [PubMed]
  4. R. H. Hildebrand, M. Dragovan, G. Novak, “Detection of Submillimeter Polarization in the Orion Nebula,” Astrophys. J. Lett, in press (1984).
    [CrossRef]
  5. S. D. Smith, “Design of Multilayer Filters by Considering Two Effective Interfaces,” J. Opt. Soc. Am. 48, 43 (1958).
    [CrossRef]
  6. H. A. Macleod, Thin Film Optical Filters (American Elsevier, New York, 1969), p. 172.
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).
  8. R. Ulrich, “Far-Infrared Properties of Metallic Mesh and its Complementary Structure,” Infrared Phys. 7, 37 (1967).
    [CrossRef]
  9. R. C. McPhedran, D. Maystre, “On the Theory and Solar Application of Inductive Grids,” Appl. Phys. 14, 1 (1977).
    [CrossRef]
  10. An alternative method of calculation using waveguide techniques is presented by T. Timusk, P. L. Richards, “Near Millimeter Wave Bandpass Filters,” Appl. Opt. 20, 1355 (1981).
    [CrossRef] [PubMed]
  11. Buckbee-Mears Corp, Minneapolis, Minn.
  12. S. Whitcomb, J. Keene, “Low-Pass Interference Filters for Submillimeter Astronomy,” Appl. Opt. 19, 197 (1980).
    [CrossRef] [PubMed]

1981 (1)

1980 (1)

1979 (1)

G. D. Holah, B. Davis, N. D. Morrison, “Narrow-Bandpass Filters for the Far-Infrared using Double-Half-Wave Designs,” Infrared Phys. 19, 639 (1979).
[CrossRef]

1977 (1)

R. C. McPhedran, D. Maystre, “On the Theory and Solar Application of Inductive Grids,” Appl. Phys. 14, 1 (1977).
[CrossRef]

1976 (1)

1967 (1)

R. Ulrich, “Far-Infrared Properties of Metallic Mesh and its Complementary Structure,” Infrared Phys. 7, 37 (1967).
[CrossRef]

1963 (1)

R. Ulrich, K. F. Renk, L. Genzel, “Tunable Submillimeter Interferometers of the Fabry-Perot Type,” IEEE Trans. Microwave Theory Tech. MTT-11, 363 (1963).
[CrossRef]

1958 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).

Davis, B.

G. D. Holah, B. Davis, N. D. Morrison, “Narrow-Bandpass Filters for the Far-Infrared using Double-Half-Wave Designs,” Infrared Phys. 19, 639 (1979).
[CrossRef]

Dragovan, M.

R. H. Hildebrand, M. Dragovan, G. Novak, “Detection of Submillimeter Polarization in the Orion Nebula,” Astrophys. J. Lett, in press (1984).
[CrossRef]

Genzel, L.

R. Ulrich, K. F. Renk, L. Genzel, “Tunable Submillimeter Interferometers of the Fabry-Perot Type,” IEEE Trans. Microwave Theory Tech. MTT-11, 363 (1963).
[CrossRef]

Hildebrand, R. H.

R. H. Hildebrand, M. Dragovan, G. Novak, “Detection of Submillimeter Polarization in the Orion Nebula,” Astrophys. J. Lett, in press (1984).
[CrossRef]

Holah, G. D.

G. D. Holah, B. Davis, N. D. Morrison, “Narrow-Bandpass Filters for the Far-Infrared using Double-Half-Wave Designs,” Infrared Phys. 19, 639 (1979).
[CrossRef]

Keene, J.

Macleod, H. A.

H. A. Macleod, Thin Film Optical Filters (American Elsevier, New York, 1969), p. 172.

Maystre, D.

R. C. McPhedran, D. Maystre, “On the Theory and Solar Application of Inductive Grids,” Appl. Phys. 14, 1 (1977).
[CrossRef]

McPhedran, R. C.

R. C. McPhedran, D. Maystre, “On the Theory and Solar Application of Inductive Grids,” Appl. Phys. 14, 1 (1977).
[CrossRef]

Morrison, N. D.

G. D. Holah, B. Davis, N. D. Morrison, “Narrow-Bandpass Filters for the Far-Infrared using Double-Half-Wave Designs,” Infrared Phys. 19, 639 (1979).
[CrossRef]

Novak, G.

R. H. Hildebrand, M. Dragovan, G. Novak, “Detection of Submillimeter Polarization in the Orion Nebula,” Astrophys. J. Lett, in press (1984).
[CrossRef]

Renk, K. F.

R. Ulrich, K. F. Renk, L. Genzel, “Tunable Submillimeter Interferometers of the Fabry-Perot Type,” IEEE Trans. Microwave Theory Tech. MTT-11, 363 (1963).
[CrossRef]

Richards, P. L.

Smith, S. D.

Stier, M. T.

Timusk, T.

Traub, W. A.

Ulrich, R.

R. Ulrich, “Far-Infrared Properties of Metallic Mesh and its Complementary Structure,” Infrared Phys. 7, 37 (1967).
[CrossRef]

R. Ulrich, K. F. Renk, L. Genzel, “Tunable Submillimeter Interferometers of the Fabry-Perot Type,” IEEE Trans. Microwave Theory Tech. MTT-11, 363 (1963).
[CrossRef]

Whitcomb, S.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).

Appl. Opt. (3)

Appl. Phys. (1)

R. C. McPhedran, D. Maystre, “On the Theory and Solar Application of Inductive Grids,” Appl. Phys. 14, 1 (1977).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

R. Ulrich, K. F. Renk, L. Genzel, “Tunable Submillimeter Interferometers of the Fabry-Perot Type,” IEEE Trans. Microwave Theory Tech. MTT-11, 363 (1963).
[CrossRef]

Infrared Phys. (2)

G. D. Holah, B. Davis, N. D. Morrison, “Narrow-Bandpass Filters for the Far-Infrared using Double-Half-Wave Designs,” Infrared Phys. 19, 639 (1979).
[CrossRef]

R. Ulrich, “Far-Infrared Properties of Metallic Mesh and its Complementary Structure,” Infrared Phys. 7, 37 (1967).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (4)

H. A. Macleod, Thin Film Optical Filters (American Elsevier, New York, 1969), p. 172.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1980).

R. H. Hildebrand, M. Dragovan, G. Novak, “Detection of Submillimeter Polarization in the Orion Nebula,” Astrophys. J. Lett, in press (1984).
[CrossRef]

Buckbee-Mears Corp, Minneapolis, Minn.

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Figures (8)

Fig. 1
Fig. 1

(a) Schematic of a double-halfwave filter: 1,2,3, partially reflecting surfaces made of metal meshes. Surfaces 1,2 and 2,3 both form Fabry-Perot filters. Surface 2 is the reflector common to both. (b) Schematic drawing of interfering beams showing phase changes θ and ϕ as the wave propagates through the system. (The wave is shown incident at an angle only to clarify the diagram. The discussion in the text applies to normal incidence.)

Fig. 2
Fig. 2

(a) Submillimeter atmospheric windows at 350 and 450 μm at the summit of Mauna Kea, Haw. (4200 m) under 1 mm of water vapor. (b) DHW filters constructed to fit in these windows: solid curve, λ0 = 345 μm, Δλ/λ = 0.11; broken curve, λ0 = 444 μm, Δλ/λ = 0.10. The mechanical properties of these filters are the same as listed in Table I; only the grid separation has been changed to match the filter passband to the atmospheric window.

Fig. 3
Fig. 3

Assembly of an individual reflecting element. The nylon ring is forced over the snout of the stainless steel flange, thus folding the edges of the metal mesh around the snout and pressing them tightly against the stainless surface. The coefficients of thermal expansion of the materials are such that the mesh is more tightly clamped and stretched as the filter cools.

Fig. 4
Fig. 4

Assembly of reflecting elements and spacers to form the double-halfwave filter.

Fig. 5
Fig. 5

Transmission and reflection of grids used in DHW filter. Note the resonance which occurs at 65 cm−1. This is a real effect which occurs at λ/g = 1.5 for all grids tested (g = grid period): (a) g = 150 μm,a/g = 0.18; (b) g = 50 μm,a/g = 0.28 (a is wire width).

Fig. 6
Fig. 6

(a) Measured spectra of completed DHW filter. The spectra were measured in a high f/No. beam (f/90). (b) Calculated spectra using procedure described in the text and measured optical properties of the grids (Fig. 5). Diffraction of the incident wave must be taken into account for frequencies of >80 cm−1. The transmission properties cannot be modeled by simple multiple-beam interference at higher frequencies. A low-pass filter is used to reject all but the fundamental (n = 1) mode.12

Fig. 7
Fig. 7

(a) Transmission of one Fabry-Perot cavity used in the DHW filter. (b) Transmission of the DHW filter. Note the squarer pass-band and better out-of-band rejection compared with a single Fabry-Perot.

Fig. 8
Fig. 8

Amplitudes t,s plotted in the complex plane.

Tables (1)

Tables Icon

Table I Mechanical Characteristics of DHW Filter

Equations (5)

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T ( ω ) = T 1 ( ω ) T 2 ( ω ) 1 - 2 R 1 ( ω ) R 2 ( ω ) cos ( ϕ 1 + ϕ 2 - Δ 1 ) + R 1 ( ω ) R 2 ( ω ) ,
T D H W ( ω ) = T F P ( ω ) T 3 ( ω ) 1 - 2 R F P ( ω ) R 3 ( ω ) cos ( ϕ F P + ϕ 3 - Δ 2 ) + R F P ( ω ) R 3 ( ω ) ,
t ( ω ) 2 + s ( ω ) 2 = 1.
x 2 + y 2 + x = 0.
t · s = ( x , y ) · ( 1 + x , y ) = x 2 + y 2 + x .

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