Correlated Photon System Measures Radiance Directly, Part II

The second part of this article describes an experimental system that implements the correlated photon method for absolute infrared spectral irradiance measurements. Part I (Correlated Photon System Measures Radiance Directly, Part I) discusses the physical mechanism and error sources for the technique.

By: Alan Migdall, National Institute of Standards and Technology

Contents
System design
Measurement function: bandpass and overlap
Correlated method radiance determination
Correlated versus conventional measurements

System design
We used the correlated photon technique to measure the radiance of a conventionally-calibrated, high-temperature argon discharge arc source at two infrared (IR) wavelengths. This is the first time that this method has been used to provide absolute radiance measurements of a source that has been conventionally calibrated, providing a good accuracy test of the method and revealing unexpected systematic effects.

We used an argon ion laser operating at 457.9-nm to pump a LiIO₃ crystal that was oriented to produce correlated visible/IR photon pairs. For our radiance measurements, we selected pairs of photons at two different sets of visible/IR wavelengths: 0.5288 µm/3.415 µm and 0.5065°µm/4.772°µm, where the second wavelength of each pair is the wavelength at which the IR radiance was measured.

All detection was done at visible wavelengths, using a silicon avalanche photodiode (APD). A pinhole near the detector defined the detector collection angle. Two different visible interference filters centered at 528.8 nm and 506.5 nm were used individually to limit light on the APD. The peaks of these visible passbands defined the wavelengths of the radiance calibrations to be 3.415°µm and 4.772°µm respectively.

The IR source measured was a high temperature argon arc discharge source producing an equivalent black body temperature of ~4000 K to 7000 K in the spectral region of interest. Because the arc emits prodigious amounts of visible and ultraviolet (UV) light as well as IR, a blocking filter was used to limit the arc output to wavelengths longer than 1°µm.⁶ The output of the arc was imaged into the crystal with an infrared lens; a shutter turned the IR input to the crystal on and off.

The conventional determination of the arc's spectral radiance was made with an IR spectrometer and detector system by comparison to a blackbody source. ⁷

Measurement function: bandpass and overlap
To understand these measurements, we must consider two components of the measurement function. First, the method requires knowledge of the IR measurement bandpass. Second, the overall efficiency of the measurement is affected by how completely the IR input beam illuminates the crystal region pumped by the pump laser.

The bandpass of the IR radiance measurement was defined by the IR wavelengths corresponding to the half maximum points of the visible bandpass. This visible detection bandwidth was determined from the smaller of two limits: a filter limit and a geometrical limit. The first, Dl_vis(filter), is just the bandpass of the visible interference filter in front of the APD. The second, Dl_vis(geom), is due to the range of down-conversion angles seen by the detector and the angle vs. visible wavelength dispersion of the down-converted light, dq(l_vis)/dq_vis.Of the two IR radiance measurements in our tests, one was dominated by the visible spectral filter and one by the geometric limit.

Ideally, the pumped region of the crystal should be uniformly illuminated by the IR radiation to be measured. Due to the length of the crystal and the sizes of the pump and IR beams, it was not possible to achieve complete uniformity of illumination, so a calculation of an overlap factor was required. The goal here is to design a system where the overlap factor approaches unity so that the effect of calculational uncertainty on the final result is small. For the two measurements reported, we achieved overlap factors in the 0.85 to 0.95 range.

Correlated method radiance determination
As stated, the absolute radiance of the arc in photons/mode is simply the ratio of the correlated visible signal produced with arc shutter open, to the signal with the arc shutter closed minus one. Because the radiance measured is actually the radiance at the crystal, an additional term is required to obtain the radiance of the arc at its origin, a throughput or total system efficiency factor. The radiance (in photons/mode) of the arc at its origin is then:

where n₁ (on) and n₁ (off) are the visible PDC signals with the arc shutter open and closed and e is the total system efficiency. This efficiency factor contains all systematic effects such as beam overlap factors and measured IR beam loss (defined as attenuation of the IR signal in its trip from the arc to the center of the crystal, which includes filter, lens, and crystal transmittance losses).

We calculated the overlap integral and optimized it with respect to parameters such as angular alignment, translational position, and image magnification. The result of this optimization yielded maximum ratios of 0.4381 and 0.9380 for the 3.415°µm and 4.772°µm measurements respectively (see table). It is worth noting that these ratios, of order unity, are the largest thermally-stimulated steady-state down-conversion signals ever produced. ^{4, 8}

The actual arc radiances are then these ratios divided by the system efficiencies, yielding radiances of 0.5894±0.0117 photon/mode and 1.5886±0.0186 photon/mode at 3.415°µm and 4.772°µm respectively (these are relative standard uncertainties).

Correlated versus conventional measurements
The two measurement methods agreed to approximately 3% which is also the average uncertainty of the comparisons at the two measurement wavelengths. A major source of uncertainty in the comparison was the uncertainty of the conventional measurement, which could be reduced by either monitoring the arc source for variations while making the comparison or switching to a more stable source.

For the correlated measurement, the determination of the system efficiency was the major source of uncertainty. Using a shorter crystal would move the overlap closer to unity, providing a commensurate reduction in the uncertainty. Also, moving to a redder pump would reduce the IR beam angles, further improving the overlap. This change might also allow the use of a crystal with transmittance further into the IR, which would reduce the uncertainty. With these improvements the verification of the correlated photon method could likely be pushed to better than 1%, as well as allowing measurements to be made beyond 5µm.

The correlated photon has two unique advantages: it allows the IR measurement problem to be shifted into the visible where better radiometric detectors are available, and it allows the measurement of spectral radiance directly, without having to measure power and geometrical quantities and inferring spectral radiance. This independence of method alone makes the correlated radiance technique a useful addition to radiometry. The results of our work show that correlated photons can indeed be a useful tool in radiometry and that the method holds enough promise that further studies are warranted.

References
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5. J.E. Midwinter and J. Warner, "The Effects Of Phase Matching Method And Of Uniaxial Crystal Symmetry On The Polar Distribution Of Second-Order Non-Linear Optical Polarization," Brit. J. Appl. Phys. 16, 1135-1142 (1965).
6. J.M. Bridges and A.L. Migdall, "Characterization Of Argon Arc Source In The Infrared," Metrologia, 32, 625-628 (1995/96).
7. A.L. Migdall et. al., "Cryogenic Optical Systems and Instruments VI," Eds., Heaney, J. and Burriesci, L., SPIE Vol 2227, p.46-53 (1994).
8. A.N. Penin et. al., "Nondestructive Measurement of Intensity of Optical Fields Using Spontaneous Parametric Down Conversion," Proc. of Quantum Electronics and Laser Science Conference 91 Baltimore, MD, p.110-112 (1991).
9. B.N. Taylor and C.E. Kuyatt, "Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results," NIST Tech. Note 1297, p. 3(1994).
10. J. Walker, R.D. Saunders, and A.T. Hattenburg, "Spectral Radiance Calibrations," NBS Special Publication 250-1, p.A-4 (1987).

About the author…
A. Migdall is with the Optical Technology Division, 221/B208, National Institute of Standards and Technology, Gaithersburg, MD 20899.