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APPARATUS FOR PERFORMING MEASUREMENTS AND ERROR ANALYSIS OF THE MEASUREMENTS
BACKGROUND OF THE INVENTION
This invention relates in general to measuring instruments and in particular to measuring instruments capable of performing error analysis of the results of measurements. All measurements contain errors from *° sources such as background effects. These effects are typically eliminated by performing a background measurement in which no sample is present and subtracting the background result from the results of all subsequent measurements. Instrument response can also vary so 15 that typically the results of sample measurements are normalized against the results of a reference measurement in which a reference substance is measured. In general, the normalized result is some function of the ratio between the background corrected sample result 20 and the background corrected reference result. For example, in analysis on a spectrophotometer the normalized result is the transmittance T and is calculated from the result S of a sample measurement, the result R of a reference measurement, and the result D of a back- 25 ground measurement by the relation T=(S-D)/(R-D).
Normalized results such as T still contain errors due to a variety of sources. For example, in a spectrophotometer the sample and reference can vary chemically 30 or physically, the optical source can vary in intensity, and the optical detector can vary in sensitivity. If these parameters vary significantly on a time scale which is less than the total measurement time, then these effects will produce errors in the normalized result. In addi- 35 tion, the sample being tested or the measurement process employed can have inherent statistical fluctuations which produce measurement error. For example, in radioactive decay processes, the number of decays per second contains an inherent fluctuation. In measure- 40 ments with a spectrophotometer, the photodetectors have an inherent variation because photons striking the detector have a probability less than one of being detected and because shot noise produces variations.
In order to judge the validity of the normalized result 45 it is necessary to know the variance of the result. In general the variance is determined by performing a series of measurements and applying well known equations to calculate the average and variance of the results of the measurements. This error analysis process has 50 even been automated on a number of devices including several brands of pocket calculators.
So if measuring instruments are well known and automated error analysis is well known, what's spe cial about combining measurement and error analysis in one 55 instrument? There are actually a number of benefits to combining both capabilities in a single instrument if the combination is achieved in the right manner. If the calculation process is not merged with the measurement process then an inordinately large memory would be 60 required to hold the data from which the average and variance are calculated. In a practical sense, the amount of data is too large for separate acquisition and statistical data manipulation to be usable. This problem is especially acute in instruments, such as a spectropho- 65 tometer, which produce spectral data. Each spectral measurement actually consists of data at a large set of points. For example, if a spectrophotometer measures
absorbance at 400 different wavelengths and only ten measurements are performed for each of S, R, and D, then 12,000 pieces of data must be stored for error analysis.
In order to merge the calculation process with the measurement process, the calculation process must be at least as fast as the measurement process. But to keep instrument cost down and to improve instrument speed, the central processing unit (CPU) which performs the error calculations should be available in any period in which calculations are not being performed to direct instrument control or perform non-error analysis calculations. The CPU should also control the ordering of sample, reference, and dark measurements to minimize or eliminate effects due to instrument response variation. The measurement and analysis processes also should be merged in a way which allows selection of a range of measurement integration times to enable the user to select a long enough time to reduce the variance to an acceptable level.
SUMMARY OF THE INVENTION
An instrument is presented which performs a series of sample, reference, and dark (i.e. background) measurements to generate a normalized result. The results of the sample measurements_are automatically processed to generate the average S and variance VS of the sample measurements. Likewise the average R and variance VR of the reference measurements and the average D and variance VD of the dark measurements are generated. These results are then used to calculate the average and variance of the normalized measurement result.
The calculations and measurement control are performed by a central processing unit (CPU). The measuring section of the instrument and the CPU are interfaced in a structure which enables various goals to be achieved. The primary routine of the CPU has 2 modes: the calculation mode in which the CPU performs various calculations including error analysis; and the standby mode in which the CPU is waiting for a calculation request. This primary routine is periodically interrupted to see if a measurement is to be performed. If no measurement is to be performed or if the measurement is completed then the CPU returns to performance of the primary routine. This scheme of interrupted routine execution allows efficient use of the CPU and avoids the delay which would be required if the calculations had to be completed before another measurement could be performed. This elimination of such delays allows reduction of the time between measurements thereby reducing the amount of variation of instrument response between measurements.
The sample, reference, and dark measurements are also controlled in a way which eliminates the effect of instrument response variation from the calculated normalized result and also allows the user to select a measurement routine which is long enough to reduce the variance of the normalized result to an acceptable level. These objectives are achieved by employing a set of subroutines which are selected in response to user commands and which perform sample, reference, and dark measurements throughout the measurement interval.
DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic representation of a measurement section suitable for use in a spectrophotometer built in accordance with the disclosed invention.
FIG. 2 shows a block diagram of a central processing unit which implements the disclosed invention.
FIGS. 3A-3F present flow diagrams of the subroutines employed in the Measurement Control Section.
FIG. 4 shows a keyboard suitable for input to the central processing unit.
DESCRIPTION OF THE PREFERRED
In accordance with the illustrated preferred embodiment, a spectrophotometer is presented which performs measurement routines in which a series of sample, reference^and dark measurements are performed. The average S and_variance VS of the sample measurements, the average R and varianceJVR of the reference measurements, and the average D and variance VD of the dark measurements are separately calculated for use in calculating the average A and variance VA of the absorbance of the sample substance. The absorbance and its variance are calculated in a central processing unit (CPU) using the equations:
These calculations are performed at each wavelength in the spectral range of the spectrophotometer to generate an absorbance spectrum and its variance. The spectrophotometer can also include the capability of generating a balance spectrum Bjtnd its variance VB by use of the above equations for A and VA to correct for mismatch between sample and reference cells. This procedure is disclosed in U.S. application Ser. No. 112,966 entitled Multibeam Spectrophotometer For Producing Balanced Spectra filed by Barry G. Willis et al on Jan. 15, 1980. In such a spectrophotometer the balanced spectra Ab and Vab are calculated as A#=A — B and VAB=VA+VB.
This method for calculating the average and variance of a series of measurements has application to measuring instruments other than spectrophotometers and a spectrophotometer is presented only as a concrete example of the invention. In general, in any type of measurement, background effects are eliminated by performing 45 a measurement with no sample present and subtracting the result from subsequent measurements in which a sample or reference substance is present. A normalized result is then calculated from the background corrected sample and reference measurements. The average and variance of the normalized result for a set of measurements can be calculated from the average and variance of sample, reference, and background measurements. In a spectrophotometer, the background measurement is referred to as the dark measurement and the normalized result is called the transmittance T. The transmittance is related to the absorbance by the relation A= — log T.
instrument response variation arises from several factors including variations in optical source intensity, detector sensitivity, and detector signal amplification. These three factors appear as a multiplicative factor in the result of a measurement, so that the result S of a sample measurement can be written as S=ajS where as is the instrument response factor and s is the factor representing actual sample transmittance. Similarly the result R of a reference measurement can be written as R=arr and the result D of a dark measurement can be written as D=cyd. The subscripts s, r, and d on these variables indicates that these measurements are performed at 3 distinct times.
The instrument response factor will cancel out of the calculations of absorbance only if the sample reference and dark measurements are completed in an interval which is short compared to the characteristic time t/ of variation of the instrument response factor so that as. =ar=ad
Accuracy is therefore improved in a spectrophotometer capable of performing all sample, reference, and dark measurements in an interval which is short compared to t/. However, the reduction of variance to desired levels often requires a total number of measurements extending over an interval which is longer than tj so that it is important to perform the series of measurements in a way which continues to allow cancellation of the instrument response factor. This cancellation is achieved by performing individual measurements in an interval which is short compared to t/ and also performing sample, reference, and dark measurements throughout the entire measurement interval. To see that this procedure leads to cancellation of the instrument response function note that the variation of as and the variation of s are statistically independent so that the average of S equals the product of the average of as timesjhe average of s (i.e. S=ass). Similarly, R=arT and D=cyd. Because all three type of measurements are performed throughout the measurement interval, the average values as, ar, and ad of the instrument re, sponse factors are equal and cancel out of the calculations of A and VA.
An optical measurement section 10 having sample, reference, and dark positions such as the optical section presented in U.S. Pat. No. 4,227,079 entitled Multipath Fine Positioning Beam Director issued to Dukes et al. on Oct. 7, 1980, is employed in a spectrophotometer built in accordance with the disclosed invention to enable sample, reference, and dark measurements to be performed in any selected order of performance. Measurement section 10 is illustrated schematically in FIG. 1. An optical beam 12 is produced by a source 11 and is directed by a beam director 13 along one of the following paths: a reference path 14 through a reference cell 15; a dark path 16 to a dark position 17; or a sample path 18 through a sample cell 19. The beam then strikes a dispersive element 110 and is dispersed to a photodiode detector array 111. The measurement results are transferred to a central processing unit (CPU) 112 for analysis and processing. An output section such as cathode ray tube (CRT) 113 is included to display the results processed by the CPU. An input section such as keyboard 114 is included to enable input of user commands (1) for selecting the measurement routine to be performed, (2) for initiating the execution of the measurement routine, (3) for initiating the output of data, and (4) for entering data.