Abstract

Placement of a scatter cone at the center of the secondary of a Cassegrain telescope greatly reduces Narcissus reflection. To calculate the remaining Narcissus reflection, a time-consuming physical optics code such as GRASP8 is often used to model the effects of reflection and diffraction. Fortunately, the Cassegrain geometry is sufficiently simple that a combination of theoretical analysis and Fourier propagation can yield rapid, accurate results at submillimeter wavelengths. We compare these results with those from GRASP8 for the heterodyne instrument for the far-infrared on the Herschel Space Observatory and confirm the effectiveness of the chosen scatter cone design.

© 2005 Optical Society of America

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References

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  1. Th. De Graauw, F. P. Helmich, “Herschel-HIFI: the heterodyne instrument for the far-infrared,” in The Promise of the Herschel Space Observatory, G. L. Pilbratt, J. Cernicharo, A. M. Heras, T. Prusti, R. Harris, eds., SP-460, 45–51 (European Space Agency, 2001).
  2. G. L. Pilbratt, “Herschel Space Observatory mission overview,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 586–597 (2003).
    [CrossRef]
  3. E. Sein, Y. Toulemont, F. Safa, M. Duran, P. Deny, D. de Chambure, T. Passvogel, G. L. Pilbratt, “A Φ3.5m SiC telescope for Herschel mission,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 606–618 (2003).
    [CrossRef]
  4. A. Poglitsch, C. Waelkens, N. Geis, “The Photodetector Array Camera and Spectrometer (PACS) for the Herschel Space Observatory,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 662–673 (2003).
    [CrossRef]
  5. M. J. Griffin, B. M. Swinyard, L. G. Vigroux, “SPIRE—Herschel’s Submillimetre Camera and Spectrometer,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 686–697 (2003).
    [CrossRef]
  6. R. J. Allen, “The radio spectrum of Virgo A from 1411.7 to 1423.8 MHz,” Astron. Astrophys. 3, 316–322 (1969).
  7. D. Morris, “Chromatism in radio telescopes due to blockage and feed scattering,” Astron. Astrophys. 67, 221–228 (1978).
  8. S. Silver, Microwave Antenna Theory and Design (McGraw-Hill, 1949); reprinted by Peter Peregrinus, London, in 1984 as Vol. 19 of the EEE Electromagnetic Waves Series).
  9. R. Padman, R. E. Hills, “VSWR reduction for large millimeter-wave cassegrain radiotelescopes,” Int. J. Infrared Millim. Waves 12, 589–599 (1991).
    [CrossRef]
  10. G. T. Poulton, S. H. Lim, “Calculation of input-voltage standing-wave ratio for a reflector antenna,” Electron. Lett. 8, 610–611 (1972).
    [CrossRef]
  11. C. Dragone, D. C. Hogg, “The radiation pattern and impedance of offset and symmetrical near-field Cassegrainian and Gregorian antennas,” IEEE Trans. Antennas Propag. AP-22, 472–475 (1974).
    [CrossRef]
  12. A. R. Lopez, “The geometrical theory of diffraction applied to antenna pattern and impedance calculations,” IEEE Trans. Antennas Propag. AP-14, 40–45 (1966).
    [CrossRef]
  13. K. Pontopiddan, ed., Technical Description of GRASP8, (TICRA Engineering Consultants, 2002), ISBN 87-989218-0-0, Sec. 2.3.1.3.
  14. P. F. Goldsmith, Quasioptical Systems; Gaussian Beam Quasioptical Propagation and Applications (Institute of Electrical and Electronics Engineers, 1998).
  15. G. E. Sommargren, H. J. Weaver, “Diffraction of light by an opaque sphere. 1: Description and properties of the diffraction pattern,” Appl. Opt. 29, 4646–4657 (1990).
    [CrossRef] [PubMed]
  16. J. W. Goodman, Introduction to Fourier Optics (Wiley1968), Secs. 3.7 and 5.1.

1991 (1)

R. Padman, R. E. Hills, “VSWR reduction for large millimeter-wave cassegrain radiotelescopes,” Int. J. Infrared Millim. Waves 12, 589–599 (1991).
[CrossRef]

1990 (1)

1978 (1)

D. Morris, “Chromatism in radio telescopes due to blockage and feed scattering,” Astron. Astrophys. 67, 221–228 (1978).

1974 (1)

C. Dragone, D. C. Hogg, “The radiation pattern and impedance of offset and symmetrical near-field Cassegrainian and Gregorian antennas,” IEEE Trans. Antennas Propag. AP-22, 472–475 (1974).
[CrossRef]

1972 (1)

G. T. Poulton, S. H. Lim, “Calculation of input-voltage standing-wave ratio for a reflector antenna,” Electron. Lett. 8, 610–611 (1972).
[CrossRef]

1969 (1)

R. J. Allen, “The radio spectrum of Virgo A from 1411.7 to 1423.8 MHz,” Astron. Astrophys. 3, 316–322 (1969).

1966 (1)

A. R. Lopez, “The geometrical theory of diffraction applied to antenna pattern and impedance calculations,” IEEE Trans. Antennas Propag. AP-14, 40–45 (1966).
[CrossRef]

Allen, R. J.

R. J. Allen, “The radio spectrum of Virgo A from 1411.7 to 1423.8 MHz,” Astron. Astrophys. 3, 316–322 (1969).

de Chambure, D.

E. Sein, Y. Toulemont, F. Safa, M. Duran, P. Deny, D. de Chambure, T. Passvogel, G. L. Pilbratt, “A Φ3.5m SiC telescope for Herschel mission,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 606–618 (2003).
[CrossRef]

De Graauw, Th.

Th. De Graauw, F. P. Helmich, “Herschel-HIFI: the heterodyne instrument for the far-infrared,” in The Promise of the Herschel Space Observatory, G. L. Pilbratt, J. Cernicharo, A. M. Heras, T. Prusti, R. Harris, eds., SP-460, 45–51 (European Space Agency, 2001).

Deny, P.

E. Sein, Y. Toulemont, F. Safa, M. Duran, P. Deny, D. de Chambure, T. Passvogel, G. L. Pilbratt, “A Φ3.5m SiC telescope for Herschel mission,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 606–618 (2003).
[CrossRef]

Dragone, C.

C. Dragone, D. C. Hogg, “The radiation pattern and impedance of offset and symmetrical near-field Cassegrainian and Gregorian antennas,” IEEE Trans. Antennas Propag. AP-22, 472–475 (1974).
[CrossRef]

Duran, M.

E. Sein, Y. Toulemont, F. Safa, M. Duran, P. Deny, D. de Chambure, T. Passvogel, G. L. Pilbratt, “A Φ3.5m SiC telescope for Herschel mission,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 606–618 (2003).
[CrossRef]

Geis, N.

A. Poglitsch, C. Waelkens, N. Geis, “The Photodetector Array Camera and Spectrometer (PACS) for the Herschel Space Observatory,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 662–673 (2003).
[CrossRef]

Goldsmith, P. F.

P. F. Goldsmith, Quasioptical Systems; Gaussian Beam Quasioptical Propagation and Applications (Institute of Electrical and Electronics Engineers, 1998).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Wiley1968), Secs. 3.7 and 5.1.

Griffin, M. J.

M. J. Griffin, B. M. Swinyard, L. G. Vigroux, “SPIRE—Herschel’s Submillimetre Camera and Spectrometer,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 686–697 (2003).
[CrossRef]

Helmich, F. P.

Th. De Graauw, F. P. Helmich, “Herschel-HIFI: the heterodyne instrument for the far-infrared,” in The Promise of the Herschel Space Observatory, G. L. Pilbratt, J. Cernicharo, A. M. Heras, T. Prusti, R. Harris, eds., SP-460, 45–51 (European Space Agency, 2001).

Hills, R. E.

R. Padman, R. E. Hills, “VSWR reduction for large millimeter-wave cassegrain radiotelescopes,” Int. J. Infrared Millim. Waves 12, 589–599 (1991).
[CrossRef]

Hogg, D. C.

C. Dragone, D. C. Hogg, “The radiation pattern and impedance of offset and symmetrical near-field Cassegrainian and Gregorian antennas,” IEEE Trans. Antennas Propag. AP-22, 472–475 (1974).
[CrossRef]

Lim, S. H.

G. T. Poulton, S. H. Lim, “Calculation of input-voltage standing-wave ratio for a reflector antenna,” Electron. Lett. 8, 610–611 (1972).
[CrossRef]

Lopez, A. R.

A. R. Lopez, “The geometrical theory of diffraction applied to antenna pattern and impedance calculations,” IEEE Trans. Antennas Propag. AP-14, 40–45 (1966).
[CrossRef]

Morris, D.

D. Morris, “Chromatism in radio telescopes due to blockage and feed scattering,” Astron. Astrophys. 67, 221–228 (1978).

Padman, R.

R. Padman, R. E. Hills, “VSWR reduction for large millimeter-wave cassegrain radiotelescopes,” Int. J. Infrared Millim. Waves 12, 589–599 (1991).
[CrossRef]

Passvogel, T.

E. Sein, Y. Toulemont, F. Safa, M. Duran, P. Deny, D. de Chambure, T. Passvogel, G. L. Pilbratt, “A Φ3.5m SiC telescope for Herschel mission,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 606–618 (2003).
[CrossRef]

Pilbratt, G. L.

E. Sein, Y. Toulemont, F. Safa, M. Duran, P. Deny, D. de Chambure, T. Passvogel, G. L. Pilbratt, “A Φ3.5m SiC telescope for Herschel mission,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 606–618 (2003).
[CrossRef]

G. L. Pilbratt, “Herschel Space Observatory mission overview,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 586–597 (2003).
[CrossRef]

Poglitsch, A.

A. Poglitsch, C. Waelkens, N. Geis, “The Photodetector Array Camera and Spectrometer (PACS) for the Herschel Space Observatory,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 662–673 (2003).
[CrossRef]

Poulton, G. T.

G. T. Poulton, S. H. Lim, “Calculation of input-voltage standing-wave ratio for a reflector antenna,” Electron. Lett. 8, 610–611 (1972).
[CrossRef]

Safa, F.

E. Sein, Y. Toulemont, F. Safa, M. Duran, P. Deny, D. de Chambure, T. Passvogel, G. L. Pilbratt, “A Φ3.5m SiC telescope for Herschel mission,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 606–618 (2003).
[CrossRef]

Sein, E.

E. Sein, Y. Toulemont, F. Safa, M. Duran, P. Deny, D. de Chambure, T. Passvogel, G. L. Pilbratt, “A Φ3.5m SiC telescope for Herschel mission,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 606–618 (2003).
[CrossRef]

Silver, S.

S. Silver, Microwave Antenna Theory and Design (McGraw-Hill, 1949); reprinted by Peter Peregrinus, London, in 1984 as Vol. 19 of the EEE Electromagnetic Waves Series).

Sommargren, G. E.

Swinyard, B. M.

M. J. Griffin, B. M. Swinyard, L. G. Vigroux, “SPIRE—Herschel’s Submillimetre Camera and Spectrometer,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 686–697 (2003).
[CrossRef]

Toulemont, Y.

E. Sein, Y. Toulemont, F. Safa, M. Duran, P. Deny, D. de Chambure, T. Passvogel, G. L. Pilbratt, “A Φ3.5m SiC telescope for Herschel mission,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 606–618 (2003).
[CrossRef]

Vigroux, L. G.

M. J. Griffin, B. M. Swinyard, L. G. Vigroux, “SPIRE—Herschel’s Submillimetre Camera and Spectrometer,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 686–697 (2003).
[CrossRef]

Waelkens, C.

A. Poglitsch, C. Waelkens, N. Geis, “The Photodetector Array Camera and Spectrometer (PACS) for the Herschel Space Observatory,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 662–673 (2003).
[CrossRef]

Weaver, H. J.

Appl. Opt. (1)

Astron. Astrophys. (2)

R. J. Allen, “The radio spectrum of Virgo A from 1411.7 to 1423.8 MHz,” Astron. Astrophys. 3, 316–322 (1969).

D. Morris, “Chromatism in radio telescopes due to blockage and feed scattering,” Astron. Astrophys. 67, 221–228 (1978).

Electron. Lett. (1)

G. T. Poulton, S. H. Lim, “Calculation of input-voltage standing-wave ratio for a reflector antenna,” Electron. Lett. 8, 610–611 (1972).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

C. Dragone, D. C. Hogg, “The radiation pattern and impedance of offset and symmetrical near-field Cassegrainian and Gregorian antennas,” IEEE Trans. Antennas Propag. AP-22, 472–475 (1974).
[CrossRef]

A. R. Lopez, “The geometrical theory of diffraction applied to antenna pattern and impedance calculations,” IEEE Trans. Antennas Propag. AP-14, 40–45 (1966).
[CrossRef]

Int. J. Infrared Millim. Waves (1)

R. Padman, R. E. Hills, “VSWR reduction for large millimeter-wave cassegrain radiotelescopes,” Int. J. Infrared Millim. Waves 12, 589–599 (1991).
[CrossRef]

Other (9)

S. Silver, Microwave Antenna Theory and Design (McGraw-Hill, 1949); reprinted by Peter Peregrinus, London, in 1984 as Vol. 19 of the EEE Electromagnetic Waves Series).

J. W. Goodman, Introduction to Fourier Optics (Wiley1968), Secs. 3.7 and 5.1.

K. Pontopiddan, ed., Technical Description of GRASP8, (TICRA Engineering Consultants, 2002), ISBN 87-989218-0-0, Sec. 2.3.1.3.

P. F. Goldsmith, Quasioptical Systems; Gaussian Beam Quasioptical Propagation and Applications (Institute of Electrical and Electronics Engineers, 1998).

Th. De Graauw, F. P. Helmich, “Herschel-HIFI: the heterodyne instrument for the far-infrared,” in The Promise of the Herschel Space Observatory, G. L. Pilbratt, J. Cernicharo, A. M. Heras, T. Prusti, R. Harris, eds., SP-460, 45–51 (European Space Agency, 2001).

G. L. Pilbratt, “Herschel Space Observatory mission overview,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 586–597 (2003).
[CrossRef]

E. Sein, Y. Toulemont, F. Safa, M. Duran, P. Deny, D. de Chambure, T. Passvogel, G. L. Pilbratt, “A Φ3.5m SiC telescope for Herschel mission,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 606–618 (2003).
[CrossRef]

A. Poglitsch, C. Waelkens, N. Geis, “The Photodetector Array Camera and Spectrometer (PACS) for the Herschel Space Observatory,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 662–673 (2003).
[CrossRef]

M. J. Griffin, B. M. Swinyard, L. G. Vigroux, “SPIRE—Herschel’s Submillimetre Camera and Spectrometer,” in IR Space Telescopes and Instruments, J. C. Mather, ed., Proc. SPIE4850, 686–697 (2003).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Schematic geometry of the scatter cone, located at the center of M2. Rays that strike the scatter cone are reflected away from the center of the focal plane.

Fig. 2
Fig. 2

Geometry of the focal plane and secondary mirror (the scatter cone at the center of M2 is shown in Fig. 1). r0 is the radius of M2; other dimensions are as shown. A feedhorn at point 1 illuminates the secondary mirror with an 11 dB edge taper and has a virtual image at point 2. A feedhorn at point 3 has a virtual image at point 4 and the center of illumination of the focal plane from this image is at point 5.

Fig. 3
Fig. 3

Two curves show relative intensity, [ERS(r,0)/E0]2 = attenuation, in the focal plane for a feedhorn located at the center of the focal plane, obtained by the NRL calculation and by GRASP8. The match between the curves validates the NRL calculation except in the region near the center. The dashed line shows relative intensity, [EG2(r,0)/E0]2, for a large, complete secondary (no beam truncation and no scatter cone). The vertical lines marked FH show the center position of the feedhorn and the ±w0 waist half-diameters. The vertical lines near ±280 mm show the edges of the scatter cone’s geometric shadow.

Fig. 4
Fig. 4

Details of Fig. 3. The solid curve shows the NRL calculation, the dotted curve that of GRASP8. In this region, the NRL calculation has a higher average level and much larger oscillations than GRASP8.

Fig. 5
Fig. 5

Comparison of the NRL calculation and GRASP8 at 480 GHz and feedhorn 84 mm from the center of the focal plane. The NRL calculation has larger oscillations in the geometric shadow of the scatter cone than does GRASP8.

Tables (2)

Tables Icon

Table 1 Herschel Bands 1–6Ha

Tables Icon

Table 2 Allowable Γmax specified for the HIFI

Equations (14)

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E G 1 ( r , 0 ) = E 0 exp ( - r 2 / w 0 2 ) ,
E G 1 ( r , z ) = π w 0 2 λ z E 0 exp ( - r 2 w 2 ( z ) ) exp [ i Φ ( r , z ) ] ,
w ( Δ z ) = λ Δ z π w 0 ,
Φ ( r , z ) = k r 2 + z 2 .
S 1 = 0 E G 1 ( r , 0 ) E LO exp ( - r 2 / w 0 2 ) 2 π r d r = E 0 E LO 0 exp ( - 2 r 2 / w 0 2 ) 2 π r d r = π 2 w 0 2 E 0 E LO ,
1 s = 1 L 0 + 2 R 2 = 1 2638 mm + 2 345.2 mm = 1 162.0 mm .
E G 2 ( r , z = L 0 + s ) = E 0 m exp [ - r 2 / ( m w 0 ) 2 ] ,
E G 2 ( 0 , 0 ) = π ( m w 0 ) 2 λ ( L 0 + s ) E 0 m exp [ i Φ ( 0 , 0 ) ] = π s w 0 2 λ L 0 ( L 0 + s ) E 0 exp [ i Φ ( 0 , 0 ) ] ,
S 2 = 0 E G 2 ( 0 , 0 ) E LO exp ( - r 2 / w 0 2 ) 2 π r d r = π s w 0 2 λ L 0 ( L 0 + s ) E 0 E LO 0 exp ( - r 2 / w 0 2 ) 2 π r d r = π 2 s w 0 4 λ L 0 ( L 0 + s ) E 0 E LO .
Γ = S 2 S 1 = 2 π s w 0 2 λ L 0 ( L 0 + s ) = 2 π × 162 × 3.89 2 0.625 × 2638 × 2800 = 3.34 × 10 - 3 ,
E CS ( x , y , 0 ) = E G 2 ( x , y , 0 ) - E G 2 ( r 0 , z 1 ) × L 2 L 1 + L 2 exp ( i k L 1 ) × exp ( i π r 2 λ L 1 ) J 0 ( 2 π r 0 r λ L 1 ) ,
E C S ( x , y , 0 ) = E G 2 ( x , y , 0 ) - E G 2 ( 0 , 0 , 0 ) L 0 ( L 0 + s ) s z 1 L 2 L 1 + L 2 × exp ( - r 0 2 w 2 ( z 1 ) ) exp 2 i k L 1 × exp ( i π r 2 λ L 1 ) J 0 ( 2 π r 0 r λ L 1 ) = E G 2 ( x , y , 0 ) - 0.34 E G 2 ( 0 , 0 , 0 ) × exp 2 i k L 1 exp ( i π r 2 λ L 1 ) J 0 ( 2 π r 0 r λ L 1 ) ,
E RS ( x , y , L 0 ) = E G 2 ( x , y , L 0 ) + [ - E G 2 ( x , y , L 0 ) + E S C ( x , y , L 0 ) ] r r SC E G 2 ( x , y , L 0 ) + E FP ( x , y , L 0 ) ,
E RS ( x , y , 0 ) = E CS ( x , y , 0 ) + E FP ( x , y , 0 ) .

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