Abstract

We are developing a heterodyne detection technique to measure optical transmittance with high accuracy over an unprecedented dynamic range. We have measured filters spanning a wide range of transmittances (12 orders of magnitude) and have evaluated the absolute uncertainties and discuss the ultimate accuracies that may be achieved. Our setup uses a two-beam Mach-Zehnder interferometer with acoustooptic frequency shifting to produce a frequency difference between the two light beams. We determine the optical transmittance of a filter by inserting it into one of the interferometer arms and measuring the change in amplitude of the signal at the difference frequency on the interferometer output beam. This method allows direct comparisons between optical and rf attenuators, ultimately tying optical transmittance measurements to rf attenuation standards in an absolute way.

© 1990 Optical Society of America

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References

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  1. J. J. Snyder, “Wide Dynamic Range Optical Power Measurement Using Coherent Heterodyne Radiometry,” Appl. Opt. 27, 4465–4469 (1988).
    [CrossRef] [PubMed]
  2. Our direct detection apparatus setup is similar, in principle, to the one used in this reference. A. R. Schaefer, K. L. Eckerle, “Spectrophotomeric Tests Using a Dye-Laser-Based Radiometric Characterization Facility,” Appl. Opt. 23, 250–256 (1984).
    [CrossRef] [PubMed]
  3. G. Eppeldauer, “Measurement of Very Low Light Intensities by Photovoltaic Cells,” in Proceedings, Eleventh IMEKO Photon Detector Symposium (Weimar, G.D.R., 1984) Proc. 182.
  4. L. Z. Gacusan, S. L. Kwiatkowsli, B. J. Sullivan, J. J. Snyder, “Stray Light and Contamination in Optical Systems,” R. P. Breault, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.967, 178–182 (1989).
  5. R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), p. 195.
  6. R. H. Kingston, Detection of Optical Radiation (Springer, Berlin, 1978), p. 32.
  7. K. Tanaka, N. Ohta, “Effects of Tilt and Offset of Signal Field on Heterodyne Efficiency,” Appl. Opt. 26, 627–632 (1987), also O. E. DeLange, “Optical Heterodyne Detection,” IEEE Spectrum Vol 5 # 10 p. 77–85 (1968).
    [CrossRef] [PubMed]
  8. EG&G, Salem, MA.
  9. Certain trade names and company products are mentioned in the text or identified in an illustration to adequately specify the experimental procedure and equipment used. In no case does such identification imply recommendation or endorsement by the National Institute of Standards & Technology, nor does it imply that the products are necessarily the best available for the purpose.
  10. Analog Modules, Inc., Longwood, FL.
  11. NIST Calibration Services Users Guide 1989 Edition. J. Simmons, Ed., (Nat. Inst. Stand. Technol. Special Publication 250, revised Jan.1989), p. 154.
  12. Lucas Weinschel, Gaithersburg, MD.
  13. Hewlett-Packard Co., Loveland, CO.
  14. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 329.

1988 (1)

1987 (1)

1984 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 329.

Boyd, R. W.

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), p. 195.

Eckerle, K. L.

Eppeldauer, G.

G. Eppeldauer, “Measurement of Very Low Light Intensities by Photovoltaic Cells,” in Proceedings, Eleventh IMEKO Photon Detector Symposium (Weimar, G.D.R., 1984) Proc. 182.

Gacusan, L. Z.

L. Z. Gacusan, S. L. Kwiatkowsli, B. J. Sullivan, J. J. Snyder, “Stray Light and Contamination in Optical Systems,” R. P. Breault, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.967, 178–182 (1989).

Kingston, R. H.

R. H. Kingston, Detection of Optical Radiation (Springer, Berlin, 1978), p. 32.

Kwiatkowsli, S. L.

L. Z. Gacusan, S. L. Kwiatkowsli, B. J. Sullivan, J. J. Snyder, “Stray Light and Contamination in Optical Systems,” R. P. Breault, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.967, 178–182 (1989).

Ohta, N.

Schaefer, A. R.

Snyder, J. J.

J. J. Snyder, “Wide Dynamic Range Optical Power Measurement Using Coherent Heterodyne Radiometry,” Appl. Opt. 27, 4465–4469 (1988).
[CrossRef] [PubMed]

L. Z. Gacusan, S. L. Kwiatkowsli, B. J. Sullivan, J. J. Snyder, “Stray Light and Contamination in Optical Systems,” R. P. Breault, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.967, 178–182 (1989).

Sullivan, B. J.

L. Z. Gacusan, S. L. Kwiatkowsli, B. J. Sullivan, J. J. Snyder, “Stray Light and Contamination in Optical Systems,” R. P. Breault, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.967, 178–182 (1989).

Tanaka, K.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 329.

Appl. Opt. (3)

Other (11)

G. Eppeldauer, “Measurement of Very Low Light Intensities by Photovoltaic Cells,” in Proceedings, Eleventh IMEKO Photon Detector Symposium (Weimar, G.D.R., 1984) Proc. 182.

L. Z. Gacusan, S. L. Kwiatkowsli, B. J. Sullivan, J. J. Snyder, “Stray Light and Contamination in Optical Systems,” R. P. Breault, Ed., Proc. Soc. Photo-Opt. Instrum. Eng.967, 178–182 (1989).

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), p. 195.

R. H. Kingston, Detection of Optical Radiation (Springer, Berlin, 1978), p. 32.

EG&G, Salem, MA.

Certain trade names and company products are mentioned in the text or identified in an illustration to adequately specify the experimental procedure and equipment used. In no case does such identification imply recommendation or endorsement by the National Institute of Standards & Technology, nor does it imply that the products are necessarily the best available for the purpose.

Analog Modules, Inc., Longwood, FL.

NIST Calibration Services Users Guide 1989 Edition. J. Simmons, Ed., (Nat. Inst. Stand. Technol. Special Publication 250, revised Jan.1989), p. 154.

Lucas Weinschel, Gaithersburg, MD.

Hewlett-Packard Co., Loveland, CO.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 329.

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Figures (6)

Fig. 1
Fig. 1

Overview of the experimental apparatus. The input laser beam is spatially filtered and split into a LO beam and a signal (S) beam. The filter to be measured is put in the S beam. (a) Only the S beam is frequently shifted. (b) Both beams are shifted. The thick plate in the LO beam is used to adjust the beam overlap. The beams are recombined and imaged through a small opening in an rf shielded box onto the detector–amplifier package. The rf output amplitude is measured and recorded for the filter in and out of the test beam. Mirrors are labeled M and the input and output beam splitters are labeled BS.

Fig. 2
Fig. 2

Electronic setups for measuring the heterodyne signal power are shown. (a) VM7 attenuation and signal calibrator. (b) HP 3585A spectrum analyzer with rf step attenuator and 35-dB amplifier.

Fig. 3
Fig. 3

Difference between the heterodyne measurement made with the attenuator and signal calibrator and the direct detection attenuation measurement is shown. The error bars are the quadrature sum of the estimated uncertainties of the conventional and heterodyne measurements.

Fig. 4
Fig. 4

Relative transmittance uncertainty (ΔT/T) of individual measurements taken with the rf spectrum analyzer setup of Fig. 2(b) are shown. The effective rf spectrum analyzer bandwidth was to 5.5 Hz. The laser power in the LO beam was 0.35 mW and the unattenuated signal beam power was 0.082 mW.

Fig. 5
Fig. 5

Heterodyne signal in dBs vs tilt of plate in the LO beam perpendicular the propagation direction. (a) Fine resolution scan showing the interference effect seen with the single frequency shift optical apparatus of Fig. 1(a). (b) Broad low resolution scan of tilt in 2 dimensions taken with the dual frequency shift apparatus of Fig. 1(b) showing parabolic peak with broad fringes superimposed.

Fig. 6
Fig. 6

Estimated systematic uncertainties of optical density measurements made using the heterodyne technique is plotted vs optical density (exclusiveof statistical uncertainties of the rf power determination). The dotted line shows the estimated 1-σ variation of transmitted intensity due to etaloning resulting from interreflections between the two filter surfaces. The dashed line is the estimated 1-σ accuracy of the VM7 rf signal calibrator. The solid line is the quadrature sum of these two uncertainties.

Tables (1)

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Table I 1σ Optical Density Uncertaintles for OD3

Equations (7)

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I ( x , y , t ) E LO ( x , y , t ) + E S ( x , y , t ) 2 .
i ( t ) = H 1 / 2 K [ 1 + T P S / P LO + 2 ( T P S / P LO ) 1 / 2 cos ( Δ t ) ] ,
i n 2 = 2 P LO e 2 η B / ω ,
i s 2 = 2 e 2 η 2 H T P LO P S / ( ω ) 2
H = | A E LO ( x , y ) E S * ( x , y ) d x d y | 2 A E LO ( x , y ) E LO * ( x , y ) d x d y A E S ( x , y ) E S * ( x , y ) d x d y .
H exp ( - k 2 r 2 α 2 / 4 ) ,
r = ( 1 / r LO 2 + 1 / r S 2 ) - 1 / 2 .

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