Substitution errors

Reference and sample measurements are performed consecutively, and the resultant (sample) spectrum is obtained as the ratio of the two photon fluxes onto the detector. In a single-beam spectrometer, there are no other options in a double-beam spectrometer, the photon fluxes of the sample and reference beam path are compared. When an integrating sphere is used with two ports and a white standard in the reference position, the photon fluxes are comparable to each other, and no problems occur. Note that the ports are part of the sphere and that any material change in the reference or sample position will change the average sphere reflectance pave. The reference measurement should be conducted with exactly the same components (windows) as the sample measurement otherwise, "substitution errors" may occur. 

Pavlov, Y. I., Rogozin, I. B., Galkin, A. P., Aksenova, A. Y., Hanaoka, F., Rada, C., and Kunkel, T. A. (2002). Correlation of somatic hypermutation specificity and A-T base pair substitution errors by DNA polymerase r) during copying of a mouse immunoglobulin k light chain transgene. Proc. Natl. Acad. Sci. USA 99, 9954—9959. 

When the sample and reference are of similar reflectance the substitution error is negligible at worst, it may reach up to 10%. In quality control applications in which a threshold value is used, the substitution error can be incorporated into this threshold. For chemical analysis in which the locations of absorption peaks, not necessarily their exact absorbance values, are important the error can also be ignored. Where correction of the substitution error is necessary, a number of correction techniques are available. 

Instruments that chop between the sample beam and the reference beam have both beams present in the sphere at essentially the same time. In this case, because the sample beam and reference beam each see the same sphere, there is no substitution error. 

If a reference is used that is very close in reflectance to that of the sample, the substitution error is negligible. For samples with very low reflectance or transmittance, the substitution error will also be very small. For a sample with zero reflectance or transmittance, there is no substitution error at all. For low reflectance and transmittance samples, the substitution error is so small that it probably falls within the random noise of the instrument. 

For single-beam spheres without dummy ports in applications in which substitution error is a concern, the spheres can be calibrated with a set of standards such as one of Labsphere s Reflectance Standards Sets, which has been measured on a sphere without substitution error. With these standards, a table of measured versus actual readings can be generated and used to correct for substitution error (Fig. 9). 

In a double-beam sphere, the substitution error is eliminated by having both sample and reference on the sphere concurrently and by alternating the measurements between sample and reference, as shown in Fig. 10. 

A second problem that can be overcome is single-beam substitution error, as discussed previously. By use of a so-called dummy port, the overall throughput of the sphere can be equalized between reference and sample scans by placing the sample in the dummy port while measuring the reference, then changing the position of sample and reference for the actual sample measurement scan. This dummy port is also illustrated in Fig. 17. 

Storm, S., and Springsteen, A. W. Quantitation of Single Beam Substitution Error. Labsphere Technical Note (1996) Quantitation of Single Beam Substitution Error, Springsteen, Storm, Ricker, and Dwyer, Presented at Int l Diffuse Reflectance Conference, Chambers-burg, PA August 1996. 

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