Calibration of photographic emulsions by cubic spline functions and application in spectrochemical analysis

Abstract

Figure 9. Near-infrared photoacoustic spectrum of praseodymium oxide, Pr,Oll, from 900 t o 2820 nm made with a modulation frequency of 48 Hz, a time constant of 2.5 s, and a bandpass of 26 4 nm The UV-visible spectrum IS saturated well beyond the usual 2500-nm limit.T o illustrate the simplicity of operation, additional rare earth spectra were run. Figures 7 and 8 show the PAS spectrum of neodymium oxide again placed in a sample holder in powder form directly from the original container. Figure 8 illustrates the decrease in signal-to-noise ratio beyond 2500 nm. Similarly, Figure 9 shows the spectrum of praseodymium oxide (Pr60,,) in the near-infrared. The ultraviolet and visible spectra are saturated for this substance.Photoacoustic spectra have been obtained for a wide range of substances including textiles. paint, semiconductors, asbestos, fungi spores, paper, blood smears, and catalysts to name a very few. The number of potential applications is large, and instrumentation is becoming more readily available to make possible the exploration of these essential investigations. LITERATURE CITED(1) M.A method of computation for calibration of photographic emulsion and conversion of microphotometer readings to relative intensities on a digital computer with special application to spectrochemical analysis is descrlbed. A numerical method using cubic spline functions for the treatment of experimental data is discussed. The method extends the operational range of the quantitative determinations from the gross fog level of the emulsion to very high absorbance values approaching saturation. A program is described, that includes an emulsion calibration curve, corrections for the background, and the internal reference ratio calculations. The program provides the automatic selection of the required application through a preliminary analysis of the input data. Various algorithms are described, and some results to test the procedure are given.The use of the photographic plate as a detector has several advantages. A large portion of the spectrum can be recorded simultaneously, and a permanent record is obtained. Since the plate must be exposed for a given time, the radiation intensity is integrated over the exposure time, and random fluctuations typical of discharges are averaged and smoothed out. The outstanding limitation in the use of photographic plates, however, is the complicated relationship between the incident intensity and the consequent plate blackening, which is the information needed for quantitative analysis.The plot of absorbance as a function of the logarithm of the exposure (commonly known as a Hurter-Driffied curve) is linear for a limited region where the intensity calculation is easy so that the possibility of a further extension of this region would be extremely advantageous.In an attempt a t linearizing the calibration curve and thus also at extending the operational range, mathematical transformations of the absorbance values were made by various researchers (1-23). The results, however, were not fully ...

Use of Weighted Least-Squares Splines for Calibration in Analytical Chemistry

“…Recent results suggest that, in the absence of a good analytical model, the use of the spline functions could be a good approach in the treatment of data. Applied first in statistical sciences, spline functions became extremely important in the chemical data analysis in the last few decades. − Until now, the greatest part of successful applications of spline functions in analytical chemistry has been devoted to fields such potentiometric titrations, − spectroscopy, − X-ray spectroscopy, − and signal processing. − …”

“…Applied first in statistical sciences, spline functions became extremely important in the chemical data analysis in the last few decades. [5][6][7][8][9] Until now, the greatest part of successful applications of spline functions in analytical chemistry has been devoted to fields such potentiometric titrations, [10][11][12][13] spectroscopy, [14][15][16][17][18] X-ray spectroscopy, [19][20][21] and signal processing. [22][23][24] In the present paper least-squares splines are used instead of interpolatory ones.…”