Colorimetric Calculations Research Articles

Propagation of random errors in spectrophotometric colorimetry

AbstractEvery physical quantity with an a priori range of numerical values constituting a continuum is subject to error in its measurement. It is important to report the highest amount by which any measured quantity might be in error. Optical radiation measurements are typiclly based on determination of the ratio of the instrumental reading of a calibrated standard to the instrumental reading of the test sample. There are random and systematic errors in both the instrumental readings and the calibration values. The uncertainty in a calculated value due to random error in its constituents can be determined using well known techniques of error propagation. Examples of error propagation through spectral reflectance factor measurements and colorimetric calculations are presented. The standard deviations of CIELAB coordinates for typical measurements can be as high as 0.258 due only to random errors in the calibration chain.

The effects of bandpass intensity distribution spectrum on measurements of solid samples using a spectrofluorometer.

The monochromators used in spectrofluorometers typically behave as filters with a triangular-shaped intensity transmission spectrum, with the bandpass value referring to the width of the triangular spectrum at half the maximum intensity. The effects of the shape of the waveband upon the reflectance and fluorescence measurements made with the spectrofluorometer are discussed from a geometric point of view, particularly in relation to subsequent colorimetric calculations.

Extreme errors of numerical integrations in colorimetric calculations

The tristimulus values of object-color stimuli are commonly calculated by means of the weighted-ordinate method at constant wavelength intervals. By assuming that the tristimulus values are calculated accurately when the wavelength interval is Δλ = 5 nm, we have estimated the extreme errors that can occur when Δλ is increased to 10 and 20 nm. We have also estimated the extreme errors that can occur when other approximate numerical integrations are used, such as Simpson’s rule or Durand’s rule of integration. The extreme errors, are always very large and are caused by jagged spectral distributions of the object-color stimuli included in this study.

Theoretical Limits of Errors in Colorimetric Calculations

Theoretical Limits of Errors in Colorimetric Calculations

Discharge Lamps and Color Television

New types of high-efficiency discharge lamps are being used increasingly to light many areas, including sports stadiums and arenas where color TV pickups are often made. Colorimetric calculations and live TV tests show that, despite some color distortion due to the light-source spectra, TV color quality is adequate for remote pickups of sports and other events. Suggestions are given for lighting-system design and for meeting operational problems related to remote pickups under discharge lamps.

バラ花弁の色調発現の研究 (第7報)

The spectral characterization was made on aqueous acid extracts of the petals of red rose cultivar Happiness and those of black cultivar Bonne Nuit. When these extracts were heated at 68-75°, the spectral shift from 508mμ to 502mμ came into appearance. The wave length showing minimum transmittance of the petal extract was ca. 6mμ longer than that of the acidic solution of crystalline cyanin, i.e., an anthocyanin component of rose petals. Followingly, it is conceivable that co-pigmentation takes place in these extracts.From the comparison of spectral transmittance curves in detail, it was shown that the petal extracts exhibit some hyperchromic and bathochromic effects on anthocyanin color at pH 3, whereas only a bathochromic effect at pH 1. Colorimetric calculation based on these curves has revealed the existence of reddening effect in these extracts.No significant spectral difference was observed between the petal extracts of red and black cultivars. This fact seems to indicate that the co-pigmentation is not involved in an expression of the black color in rose petals.In the extracts showing an obvious spectral shift, certain flavonoids, tannins and metallic elements (K, Na, Mg, Fe, Al) have been detected. It is likely that the spectral shift observed above is due not to flavonoids and catechol tannin, but chiefly to pyrogallol tannin.

A Recording Spectrophotometer with a DigitaI Tristimulus Integrator

Toshiba Color Computer combines a recording spectrophotometer with a digital tristimulus integrator. In just two minutes the instrument records a spectral reflectance or a transmittance curve of an object in the region from 750 to 380 mμ, besides it prints out tristimulus values X, Y and S=X+Y+Z in five-digti figures.As a specially made A-D converter is used for counting the photometric wedge shift, the conversion error has been reduced to the minimum. The colorimetric calculation is carried out on the basis of a newly modified selected ordinate method, and the error of the calculation is less than 0.1 percent. Repeated measurements of color samples slightly different from each other prove that the instrument can discriminate about 100 million surface colors.

Additivity of Colour Equations

A colour can be matched by an additive mixture of three coloured lights, the most suitable being specified red, green and blue stimuli. If c1 units of one colour are matched by r1, g1 and b1 units of red, green and blue respectively, and c2 units of another colour by r2, g2 and b2 units, then according to the law of additivity of colour equations the combined colour may be matched by r1 + r2, g1 + g2 and b1 + b2 units respectively. It is the purpose of this work to investigate this law. Additivity of colour equations is implicit in all colorimetric calculations. The law is based on the results of early work done with the comparatively crude apparatus of the time, but recently these results have been questioned. The experimental work was performed on the Wright colorimeter, where colour matches were made on pairs of stimuli separately and in combination. The results showed some deviations from additivity, but on the whole these were small. Large deviations appear to be associated with poor discrimination.

Eliminating confusion in colorimetric calculations.

The clinical analyst is sometimes confused in his calculations from comparison colorimetric (or turbidimetric) readings, especially if circumstances force him to deviate slightly from the definite directions of any given method. To avoid irritation and loss of time the author keeps on his desk the following equation: F, scale reading of the standard in millimeters, usually fixed at some definite point; R, scale reading of the sample analyzed; S, concentration of the standard, usually milligrams per 100 cc.; Vu, volume of the colored (or turbid) solution as matched against the standard; Vs, volume of the standard solution; D1, volume of the sample (or the aliquot extract) taken for analysis; D2, volume to which D1 is diluted before developing color (or precipitating); V, the volume of D2 used in developing the color; X, the concentration of the unknown in terms comparable to S, i. e., milligrams per cc. if S is given as milligrams; multiply X by 100 if mg. per 100 cc. is required. In most routine clinical work all but the first two and last terms () are unity and out of mind. When not in unity it is more often a simple two times, a five times or a ten times dilution, but odd dilutions may occur, as, for instance, when the sample available becomes limited through accident or otherwise. The mathematics involved should not deter the technician from saving his case.