EFFECT FROM

OF ACCURACY INTERFEROGRAM

EQUIPMENT

FUNCTION

V. P. Volkova, G, and P. F. Parshin

OF

TAKING

ON T H E OF G.

READINGS

FORM

FOURIER Gorbunov,

OF

SPECTROMETER UDC 535.853A

One of the m o s t difficult problems in F o u r i e r s p e c t r o m e t r y is the l a r g e dynamic range of the a m p l i f y ing and r e c o r d i n g equipment for large a c c u r a c y of taking readings f r o m the i n t e r f e r o g r a m . By the t e r m "dynamic range" we mean the n u m b e r of different levels of the signal, which is usually equal to the ratio of the m a x i m u m signal to the r o o t - m e a n - s q u a r e noise e r r o r . However, in real i n s t r u m e n t s the potentialities of the r e c o r d i n g o r t e l e m e t e r i n g equipment a r e limited; t h e r e f o r e it is n e c e s s a r y to find an optimum r e g i m e of operation of the equipment, which will not introduce significant distortions in r e c o r d i n g i n t e r f e r o g r a m s . As a rule, the m i n i m u m amount of the i n t e r f e r o g r a m is determined by the r e c e i v e r noise and the a c c u r a c y of taking readings of the amplitudeofthe i n t e r f e r o g r a m . The m a x i m u m signal depends on the linearity of the amplifier channel and also on the a c c u r a c y of taking readings f r o m the i n t e r f e r o g r a m . In o r d e r to determine the effect of the dynamic range and the a c c u r a c y of taking readings f r o m the i n t e r f e r o g r a m we investigated the effect of the magnitude of the relative e r r o r of taking readings f r o m the i n t e r f e r o g r a m on the form of the resulting s p e c t r u m . The i n t e r f e r o g r a m was modeled on Razdan-2 c o m puter. The dispersion curve was the initial s p e c t r u m for modeling the i n t e r f e r o g r a m . The modeling was done taking account of the effect of the b a n d - p a s s e l e c t r i c a l filter and the nonuniformity of the path diff e r e n c e [1] and the readings were taken f r o m the e x t r e m u m values of the r e f e r e n c e channel in which a n a r rowband filter is used. In modeling the period of the path difference e r r o r T o is taken equal to the period of the i n t e r f e r o g r a m and the amplitude of the e r r o r ~ = 2r/X is chosen equal to 1 and 5. To obtain the same relative e r r o r the entire range of the computer grid is used, but the computation is c a r r i e d out for different a c c u r a c i e s of readings of each point of the i n t e r f e r o g r a m , i.e. the n u m b e r of significant d i g i t s o f t h e mantissa is reduced to three, two, and one. This model is conformable with the m e a s u r e m e n t s obtained with digital v o l t m e t e r with "floating decimal point" and diffferent a c c u r a c y (number of signs) of reading. The r e s u l t s of the computation showed that even a small n u m b e r of significant digits taken at each point do not affect the results of the computations. The apparent differences in the "tails" of the computed c u r v e s a r e observed only when the n u m b e r of significant digits is d e c r e a s e d to two or even one (Fig. 1). Hence the use of i n s t r u m e n t s , that allow one to obtain a relatively small a c c u r a c y in taking readings f r o m i n t e r f e r o g r a m but retain the relative magnitude of the e r r o r s of m e a s u r e m e n t s (floating decimal), is m o s t justified. However, actual construction of such i n s t r u m e n t s is also beset with g r e a t difficulties, because the required dynamic range of operation of the equipment also gets considerably widened. The dynamic range can be determined by the number of noise "quanta," where by a quantum we mean a quantity equal to the root mean square level of the noise. In this case the a c c u r a c y of taking readings f r o m the i n t e r f e r o g r a m can not exceed the value of the quantum. A change of the value of the quantum, which was used in the m e a s u r e m e n t of the amplitudes of the i n t e r f e r o g r a m , is equivalent to a change of the dynamic range andthe a c c u r a c y of readings. F o r modeling this phenomenon the noise quantum was defined as the m a x i m u m value of the i n t e r f e r o g r a m divided by 104, 10 3, 10 2, 101. The value of any ordinate of the i n t e r f e r o g r a m was determined by the c o r r e s p o n d i n g n u m b e r of quanta. Computations show that even for small resolutions distortions a r e observed in the s p e c t r u m a l r e a d y at the value of the quantum Ira/102, Translafed from Zhurnal Prikladnoi Spektroskopii, Vol. 17, No. 6, pp, 1108-1111, D e c e m b e r , 1972. Original a r t i c l e submitted October 15, 1971. 9 1974 Consultants Bureau, a division of Plenum Publishing Corporation, 227 ~est 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.

1641

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Fig. 1 Fig. 2 Fig. 1. Spectrogram on periphery without rounding off (1)and with rounding off to one decimal place of mantissa (2) ~ = ~ - ~ / ~ ) 0 ; (Aw)0 is limit of resolution. T / T 0 = 1, ~ = 1 (a) and 5 (b). Fig. 2. S p e c t r o g r a m on p e r i p h e r y for value of the quantum Im/102 (1), Ira/10 (2), and Im/103 (3), T / T 0 = 1, /~ = 1 (a) and 5 (b).

w h e r e I m is the m a x i m u m value of the i n t e r f e r o g r a m (Fig. 2). H e r e a d e c r e a s e in the signal to noise ratio o c c u r s , i.e. these distortions are s i m i l a r to noise in the s p e c t r u m . The use of a fixed n u m b e r of quanta i n c r e a s e s the required range of a c c u r a c y in m e a s u r e m e n t s , thereby imposing additional r e q u i r e m e n t s on the equipment. T h e r e f o r e it is most advisable to use recording equipment with relatively small a c c u r a c i e s of r e a d ings but with l a r g e dynamic range (floating decimal). In the development of a m e a s u r i n g equipment the limits of variation of the dynamic range can be defined using the method of m a t h e m a t i c a l modeling taking into consideration the n e c e s s a r y r e q u i r e m e n t s on the investigated s p e c t r u m .

LITERATURE 1.

V. P.

VoIkova,

in: Mathematical Modeling in Science and Technology fin Russian], Lensovet

LTI (1971), p. 20.

1642

CITED