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A test of diffraction structures at near-millimetre wavelengths
ln/rared Phjs. Vol. 25, No, 1:2, pp. 285 288. 1985
0020 0891:85 $3.00 + 0.00 Copyright ,~" 1985 P e r g a m o n Press Ltd
Printed in Great Britain. All rights reserved
A TEST OF D I F F R A C T I O N STRUCTURES AT N E A R - M I L L I M E T R E W A V E L E N G T H S A. BLANCO, S. FONTI and M. MANCARELLA Department of Physics, University of Lecce, 73100 Lecce, Italy
(Received27 July 1984) Abstract+-The problem of diffraction effects is particularly important at millimetre wavelengths. The geometrical theory of diffraction (GTD) has been a good aid in coping with this kind of problem. The application of GTD, however,has been limited to monochromaticradiation. In this paper we show by means of experimental tests that the same method, with some minor computational modifications, also can be applied successfullyin non-monochromatic systems.
INTRODUCTION The need for a reliable method for designing antennae with very low diffraction lobes is an old problem in radio measurements. In contrast, such a problem is rather new in the millimetre region where optical detectors are used. In fact, it has become particularly serious in the last few years as measurements of cosmic background radiation around the peak have been attempted. A method based on cascaded apertures has been developed by Duncan and Fonti, {xt by which it is possible to evaluate the diffraction pattern of an optical system. Such a method has been tested experimentally) 21 However, both theory and measurements refer to monochromatic radiation. The aim of this work is to extend the method to non-monochromatic radiation (which is the usual case in far-infrared (FIR) measurements) and to test the accuracy of the theoretical predictions experimentally. THEORETICAL COMPUTATIONS The comparison between theory and experimental results, according to the geometrical theory of diffraction (GTD) approach, 12) is given by
v(o)
F(O)~d
I ( 0 ) - V(O)
D
{1)
'
where V(O) and V(0) are the signals measured at an angle 0 and on the axis, respectively. F(O) is the theoretical angular distribution fnnction computed for a set of cascaded apertures using the G T D theory, f~a is the solid angle of the detector and D accounts for the fraction of the total energy contained within a circle centred on the pattern axis. 121 Since F(O) and D are wavelength dependent, for non-monochromatic radiation the comparison between theory and experiment should be made following the relation:
g(o) I ( 0 ) - V(0)
B(2, T)O(2)F(O,),)f2a/D(2) d2 i
f.'2
,
(2)
B(2, T)q~(2) d2 1
where B(2, T) is the Planck function of the source, assumed to be a black body at temperature T, ¢(2) is the spectral response of the detector, and )+1 and 22 define the wavelength range. The difference between the two computational methods is shown in Fig. 1 where the two corresponding theoretical trends are compared. Curve (a) is evaluated using equation (1) for 2 = l mm, while curve (b) is evaluated using equation (2) for 21 -- 0.2ram, 22 = 3 m m and the appropriate B(2, T) and ~b(2) (see later). Both curves refer to the same diffraction structure. We chose 2 = l m m for curve (a) since this is the effective wavelength normally assumed for our experimental 285
286
A. BI ,~N(O et al. "C
IC' 1
4
1o 5
fl 1(,
L 20
k
30
0 (d#g)
Fig. 1. Theoretical behaviour of the diffraction pattern for a double-aperture system. Curve (a) is obtMned using equation (1) for 2 = 1 mm: curve (b), using equation (2) for the non-monochromatic case.
situation. The discrepancy between the two curves clearly shows that if equation (l) is used instead of equation (2) an appropriate choice of the effective wavelength is crucial in order to make theoretical predictions for non-monochromatic measurements. MEASUREMENTS
AND RESULTS
As usual, the experiment has been carried out assuming symmetrical behaviour with respect to the interchange of detector and source (time reverse approach). The experimental setup is outlined in Fig. 2. The radiation source was a Hg arc lamp (Philips H P K 125 W). Its emission B(2, T) has been evaluated according to the effective temperature given by Kimmitfl s~ for this source. The detector used was a composite Ge bolometer working at liquid He temperature with an input optics consisting o f a n . l / 4 Winston cone collector of 18 mm dia. Its spectral response ~b().) was essentially due to the cold filter set inside the Dewar in front of the detector. During the measurements we used two different FIR filters: a low-pass filter (LP) of the type obtained by Dall'Oglio e t al, ~4~ and a band-pass filter (BP) centred at 1.3mm, supplied by the Infrared Laboratories Inc. ~s~ With the latter filter, the effective aperture of the Winston cone was 12.7 mm dia. RADIATION SHIELD (ECCOSORB)
DIFFRACTING STRUCTURE
7
BLADE CHOPPER
DETECTOR
__O--#:--
/ -
-
-
-
t - - - -
/
Hg LAMP
/
QUARTZ LENS
/ /
/
/
7
/
Fig. 2. Schematic plan vie~ of the experimental setup.
-
-
Diffraction structures at near-millimetre wavelengths
287
T h e use of a radiation shield was essential, since radiation reaching the detector w i t h o u t passing t h r o u g h the diffracting structure seriously affected the results. W e tested t w o different diffracting structures. T h e simplest consisted of a single circular aperture of 1 0 m m dia m a d e in stainless steel of 601~m thickness placed at a b o u t 4 0 0 m m from the detector. M e a s u r e m e n t s were m a d e using b o t h L P and BP filters. T h e e x p e r i m e n t a l results are s h o w n in Figs 3 and 4, respectively. 10 0
10- I
10 2
v 10 -3
10-4
10- 5
I 10
O
r 20
I 30
I 40
O (deg)
Fig. 3. Plot of the theoretical curve ( -
) and experimental points for the single-aperture diffraction system with the LP filter.
1o
10 1 10 1
\\
\l\1
10 "2 qb kt
%
10 3
!0 4
10 .4
~
I t'
i
10 51
I
40
J
20 O(deg)
I
30
Fig. 4. Same as in Fig. 3 but with the BP filter.
40-5
I 10
I 20
I 30
e (deg)
Fig. 5. Plot of the theoretical curve (-- ) and experimental points for the double-aperture diffraction system with the LP filter. For comparison, the theoretical curve for the single-aperture case is also plotted ( - ).
A. BLAN('O el al.
288
The second structure under test consisted of two centred circular apertures of 10 and 16 mm dia, again made in stainless steel and spaced 50ram apart. The smaller aperture faced the incident radiation from the source and was placed about 450 m m from the detector. This structure was tested using the LP filter only and the experimental results are shown in Fig. 5. DISCUSSION AND CONCLUSIONS As can be seen from Figs 3-5 the agreement between theoretical predictions and experimental results is quite satisfactory. The discrepancies for angles near the axis can be explained as due to the large field-of-view of the detector. For the double-aperture system the poor agreement extends to larger angles because of the presence of the transition region from the single- to double-aperture regime. 12~ It is worthwhile to note that the theoretical curves of Figs 3 and 5, computed for the two different diffracting structures, are obtained using the same spectral response q~(2) in both cases. In Fig. 4, however, the theoretical curve is considerably higher than that of the same diffracting structure in Fig. 3, as one should expect, according to the different profiles of the two filters on the short-wavelength side. We wish also to emphasize that the experimental data reported here are the average of several different measurements for each structure under test. We found that great care had to be taken in the alignment of the whole optical layout in order to obtain good reproducibility. As can be seen, in each case we reached the noise level of our detector. In the case of the doubleaperture structure and the BP filter the noise level was too close to the axis to perform measurements of some significance. We may conclude that the satisfactory agreement between theoretical predictions and experimental results enables us to state that the computational method outlined here can be successfully used to evaluate the diffraction pattern for non-monochromatic FIR experiments. ,4ckmm'ledgeme,t
This work was partially supported by the Piano Spaziale Nazionale dcl ('NR.
REFERENCES 1. 2. 3. 4. 5.
Duncan W. D. and Fonti S., D!fi'ared Ph3"s. 21, 357 (19811. Duncan W. D. and Fonti S., h!li'ared Phys. 21, 363 (1981). K i m m i n M. F.. Far Inli'ared Techniques, p. 51. Pion, London 11970}. Dall'Oglio G., Melchiorri B., De Bernardis P. and Masi S,, IJ!li'ared Phys. 22, 307 (1982). Product Brochure, Infrared Laboratories Inc., Tucson, Ariz. (June 19831.
0020 0891:85 $3.00 + 0.00 Copyright ,~" 1985 P e r g a m o n Press Ltd
Printed in Great Britain. All rights reserved
A TEST OF D I F F R A C T I O N STRUCTURES AT N E A R - M I L L I M E T R E W A V E L E N G T H S A. BLANCO, S. FONTI and M. MANCARELLA Department of Physics, University of Lecce, 73100 Lecce, Italy
(Received27 July 1984) Abstract+-The problem of diffraction effects is particularly important at millimetre wavelengths. The geometrical theory of diffraction (GTD) has been a good aid in coping with this kind of problem. The application of GTD, however,has been limited to monochromaticradiation. In this paper we show by means of experimental tests that the same method, with some minor computational modifications, also can be applied successfullyin non-monochromatic systems.
INTRODUCTION The need for a reliable method for designing antennae with very low diffraction lobes is an old problem in radio measurements. In contrast, such a problem is rather new in the millimetre region where optical detectors are used. In fact, it has become particularly serious in the last few years as measurements of cosmic background radiation around the peak have been attempted. A method based on cascaded apertures has been developed by Duncan and Fonti, {xt by which it is possible to evaluate the diffraction pattern of an optical system. Such a method has been tested experimentally) 21 However, both theory and measurements refer to monochromatic radiation. The aim of this work is to extend the method to non-monochromatic radiation (which is the usual case in far-infrared (FIR) measurements) and to test the accuracy of the theoretical predictions experimentally. THEORETICAL COMPUTATIONS The comparison between theory and experimental results, according to the geometrical theory of diffraction (GTD) approach, 12) is given by
v(o)
F(O)~d
I ( 0 ) - V(O)
D
{1)
'
where V(O) and V(0) are the signals measured at an angle 0 and on the axis, respectively. F(O) is the theoretical angular distribution fnnction computed for a set of cascaded apertures using the G T D theory, f~a is the solid angle of the detector and D accounts for the fraction of the total energy contained within a circle centred on the pattern axis. 121 Since F(O) and D are wavelength dependent, for non-monochromatic radiation the comparison between theory and experiment should be made following the relation:
g(o) I ( 0 ) - V(0)
B(2, T)O(2)F(O,),)f2a/D(2) d2 i
f.'2
,
(2)
B(2, T)q~(2) d2 1
where B(2, T) is the Planck function of the source, assumed to be a black body at temperature T, ¢(2) is the spectral response of the detector, and )+1 and 22 define the wavelength range. The difference between the two computational methods is shown in Fig. 1 where the two corresponding theoretical trends are compared. Curve (a) is evaluated using equation (1) for 2 = l mm, while curve (b) is evaluated using equation (2) for 21 -- 0.2ram, 22 = 3 m m and the appropriate B(2, T) and ~b(2) (see later). Both curves refer to the same diffraction structure. We chose 2 = l m m for curve (a) since this is the effective wavelength normally assumed for our experimental 285
286
A. BI ,~N(O et al. "C
IC' 1
4
1o 5
fl 1(,
L 20
k
30
0 (d#g)
Fig. 1. Theoretical behaviour of the diffraction pattern for a double-aperture system. Curve (a) is obtMned using equation (1) for 2 = 1 mm: curve (b), using equation (2) for the non-monochromatic case.
situation. The discrepancy between the two curves clearly shows that if equation (l) is used instead of equation (2) an appropriate choice of the effective wavelength is crucial in order to make theoretical predictions for non-monochromatic measurements. MEASUREMENTS
AND RESULTS
As usual, the experiment has been carried out assuming symmetrical behaviour with respect to the interchange of detector and source (time reverse approach). The experimental setup is outlined in Fig. 2. The radiation source was a Hg arc lamp (Philips H P K 125 W). Its emission B(2, T) has been evaluated according to the effective temperature given by Kimmitfl s~ for this source. The detector used was a composite Ge bolometer working at liquid He temperature with an input optics consisting o f a n . l / 4 Winston cone collector of 18 mm dia. Its spectral response ~b().) was essentially due to the cold filter set inside the Dewar in front of the detector. During the measurements we used two different FIR filters: a low-pass filter (LP) of the type obtained by Dall'Oglio e t al, ~4~ and a band-pass filter (BP) centred at 1.3mm, supplied by the Infrared Laboratories Inc. ~s~ With the latter filter, the effective aperture of the Winston cone was 12.7 mm dia. RADIATION SHIELD (ECCOSORB)
DIFFRACTING STRUCTURE
7
BLADE CHOPPER
DETECTOR
__O--#:--
/ -
-
-
-
t - - - -
/
Hg LAMP
/
QUARTZ LENS
/ /
/
/
7
/
Fig. 2. Schematic plan vie~ of the experimental setup.
-
-
Diffraction structures at near-millimetre wavelengths
287
T h e use of a radiation shield was essential, since radiation reaching the detector w i t h o u t passing t h r o u g h the diffracting structure seriously affected the results. W e tested t w o different diffracting structures. T h e simplest consisted of a single circular aperture of 1 0 m m dia m a d e in stainless steel of 601~m thickness placed at a b o u t 4 0 0 m m from the detector. M e a s u r e m e n t s were m a d e using b o t h L P and BP filters. T h e e x p e r i m e n t a l results are s h o w n in Figs 3 and 4, respectively. 10 0
10- I
10 2
v 10 -3
10-4
10- 5
I 10
O
r 20
I 30
I 40
O (deg)
Fig. 3. Plot of the theoretical curve ( -
) and experimental points for the single-aperture diffraction system with the LP filter.
1o
10 1 10 1
\\
\l\1
10 "2 qb kt
%
10 3
!0 4
10 .4
~
I t'
i
10 51
I
40
J
20 O(deg)
I
30
Fig. 4. Same as in Fig. 3 but with the BP filter.
40-5
I 10
I 20
I 30
e (deg)
Fig. 5. Plot of the theoretical curve (-- ) and experimental points for the double-aperture diffraction system with the LP filter. For comparison, the theoretical curve for the single-aperture case is also plotted ( - ).
A. BLAN('O el al.
288
The second structure under test consisted of two centred circular apertures of 10 and 16 mm dia, again made in stainless steel and spaced 50ram apart. The smaller aperture faced the incident radiation from the source and was placed about 450 m m from the detector. This structure was tested using the LP filter only and the experimental results are shown in Fig. 5. DISCUSSION AND CONCLUSIONS As can be seen from Figs 3-5 the agreement between theoretical predictions and experimental results is quite satisfactory. The discrepancies for angles near the axis can be explained as due to the large field-of-view of the detector. For the double-aperture system the poor agreement extends to larger angles because of the presence of the transition region from the single- to double-aperture regime. 12~ It is worthwhile to note that the theoretical curves of Figs 3 and 5, computed for the two different diffracting structures, are obtained using the same spectral response q~(2) in both cases. In Fig. 4, however, the theoretical curve is considerably higher than that of the same diffracting structure in Fig. 3, as one should expect, according to the different profiles of the two filters on the short-wavelength side. We wish also to emphasize that the experimental data reported here are the average of several different measurements for each structure under test. We found that great care had to be taken in the alignment of the whole optical layout in order to obtain good reproducibility. As can be seen, in each case we reached the noise level of our detector. In the case of the doubleaperture structure and the BP filter the noise level was too close to the axis to perform measurements of some significance. We may conclude that the satisfactory agreement between theoretical predictions and experimental results enables us to state that the computational method outlined here can be successfully used to evaluate the diffraction pattern for non-monochromatic FIR experiments. ,4ckmm'ledgeme,t
This work was partially supported by the Piano Spaziale Nazionale dcl ('NR.
REFERENCES 1. 2. 3. 4. 5.
Duncan W. D. and Fonti S., D!fi'ared Ph3"s. 21, 357 (19811. Duncan W. D. and Fonti S., h!li'ared Phys. 21, 363 (1981). K i m m i n M. F.. Far Inli'ared Techniques, p. 51. Pion, London 11970}. Dall'Oglio G., Melchiorri B., De Bernardis P. and Masi S,, IJ!li'ared Phys. 22, 307 (1982). Product Brochure, Infrared Laboratories Inc., Tucson, Ariz. (June 19831.