Abstract

For accurate measurements of chopped radiation, it is important that the photoelectric instrumentation complies with Talbot's law, that is, measures the time average. Two different photoelectric measuring systems were investigated for their compliance with Talbot's law: (1) Si photodiode with an integrating digital voltmeter (IDVM) system, and (2) Si photodiode with a lock-in amplifier. The test consisted in comparing values predicted from the amplitude and the duty factor of the chopper with values measured by both systems. It was found that the IDVM system showed satisfactory compliance with Talbot's law, whereas the lock-in system did not. However, a Fourier analysis of the signal wave shape produced correction factors for the lock-in system data which then yielded satisfactory compliance with Talbot's law.

© 1981 Optical Society of America

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References

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  1. CIE International Lighting Vocabulary, Publication CIE 17 (Bureau Central CIE, 52 Blvd. Malesherbes, 75008 Paris, 1970).
  2. J. W. T. Walsh, Photometry (Constable, London, 1958).
  3. W. Budde, Appl. Opt. 18, 1555 (1979).
  4. J. Geist, Rev. Sci. Instrum. 43, 1704 (1972).
  5. This counter was a Hewlett-Packard model 5328A Universal Counter. (The identification of products in this paper is done for completeness of the experimental description and does not constitute an endorsement by NRC or imply that this product is the best available for the purpose.)
  6. This IDVM was a Hewlett-Packard/Dymec model 2401C. Unfortunately, HP has discontinued production of this instrument. The 5328A Counter mentioned previously has a DVM option which to some extent can serve as a replacement for the HP 240 1C.
  7. Princeton Applied Research model 186A.

1979 (1)

1972 (1)

J. Geist, Rev. Sci. Instrum. 43, 1704 (1972).

Budde, W.

Geist, J.

J. Geist, Rev. Sci. Instrum. 43, 1704 (1972).

Walsh, J. W. T.

J. W. T. Walsh, Photometry (Constable, London, 1958).

Appl. Opt. (1)

Rev. Sci. Instrum. (1)

J. Geist, Rev. Sci. Instrum. 43, 1704 (1972).

Other (5)

This counter was a Hewlett-Packard model 5328A Universal Counter. (The identification of products in this paper is done for completeness of the experimental description and does not constitute an endorsement by NRC or imply that this product is the best available for the purpose.)

This IDVM was a Hewlett-Packard/Dymec model 2401C. Unfortunately, HP has discontinued production of this instrument. The 5328A Counter mentioned previously has a DVM option which to some extent can serve as a replacement for the HP 240 1C.

Princeton Applied Research model 186A.

CIE International Lighting Vocabulary, Publication CIE 17 (Bureau Central CIE, 52 Blvd. Malesherbes, 75008 Paris, 1970).

J. W. T. Walsh, Photometry (Constable, London, 1958).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of optical set up for measurement of chopped radiation (S, source; L1 and L2 lenses; C, chopper; D, detector).

Fig. 2
Fig. 2

Diagram of situation in plane of chopper blades.

Fig. 3
Fig. 3

Signal from detector during one cycle (A, amplitude; α1, duty angle; β, slope angle).

Fig. 4
Fig. 4

Schematic diagram of instrumental set up: S, source; L1, lens; C, chopper; D, detector; LED, light emitting diode; A233L, operational amplifier (Analog Devices model 233L).

Tables (4)

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Table I Fourier Factors for Eq. (3)

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Table II Talbot's Law Compliance for d = 0.50 and Different Frequencies

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Table III Measurements with the IDVM System

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Table IV Measurements with the Lock-In Amplifier

Equations (15)

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f 1 ( ϕ ) = A 2 π { π β ( π α β ) + 2 π β ϕ + sin [ 2 π β ( ϕ π 2 + α 2 ) ] } ( up slope ) ;
f 2 ( ϕ ) = A ( flat top ) ;
f 3 ( ϕ ) = A 2 π { π β ( π + α + β ) 2 π β ϕ + sin [ 2 π β ( ϕ π 2 + α 2 ) ] } ( down slope ) ;
f 4 ( ϕ ) = 0 for the remainder of the cycle ;
γ 1 ϕ γ 2
γ 2 ϕ γ 3
γ 3 ϕ γ 4
γ 1 = ( π α β ) / 2 , γ 2 = ( π α + β ) / 2 , γ 3 = ( π + α β ) / 2 , γ 4 = ( π + α + β ) / 2 .
a 0 = A 2 π ( α + β ) ,
a n = ( 2 π / β ) 2 ( 2 π / β ) 2 n 2 2 A n π sin ( n β / 2 ) n β / 2 sin ( n α / 2 ) cos ( n π / 2 ) ,
b n = ( 2 π / β ) 2 ( 2 π / β ) 2 n 2 2 A n π sin ( n β / 2 ) n β / 2 sin ( n α / 2 ) sin ( n π / 2 ) .
V m = A 2 π n ( 2 π / β ) 2 ( 2 π / β ) 2 n 2 1 n 2 sin ( n β / 2 ) n β / 2 sin ( n α / 2 ) sin ( n π / 2 ) with n = 1 , 3 , 5 , 7 , ,
S = A F ,
A d = S d F .
S 2 d F

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