Calculation of Integrated Intensities in Spectrographic Microanalysis*

J. K. Hurwitz

doi:10.1364/JOSA.44.000030

Journal of the Optical Society of America
Vol. 44,
Issue 1,
pp. 30-34
(1954)
•https://doi.org/10.1364/JOSA.44.000030

Calculation of Integrated Intensities in Spectrographic Microanalysis

J. K. Hurwitz

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J. K. Hurwitz, "Calculation of Integrated Intensities in Spectrographic Microanalysis*," J. Opt. Soc. Am. 44, 30-34 (1954)

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Abstract

The change in integrated intensity occurring when a spark traverse is made across a region in which a very high concentration gradient exists has been calculated. The theory which was developed accounted for the effect of sparked-volume size, spectrograph and microphotometer slit-lengths, and the ratio of the camera speed to the sample speed. Three separate assumptions regarding the shape of the sparked volume were made, viz., a circular disk of uniform thickness, a cap of a sphere, and a paraboloid of revolution. The disk gave good agreement only if the sample speed was sufficiently high: at lower speeds this was not true since the spark discharge remained upon any one point long enough to etch out a crater of microscopically observable size. The latter two shapes were satisfactory for all practical conditions. It is suggested that this theory may be extended to the analysis of segregates in metals and alloys even though the segregate may be considerably smaller than the sparked volume.

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Equations (19)

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b	0	1	2	3	4	5	6	7	8	9
1.0	0.0
0.9	10.0	9.0	8.0	7.0	6.0	5.0	4.0	3.0	2.0	1.0
0.8	19.9	18.9	17.9	16.9	16.0	15.0	14.0	13.0	12.0	11.0
0.7	29.6	28.7	27.7	26.7	25.8	24.8	23.8	22.8	21.9	20.9
0.6	39.0	38.1	37.2	36.2	35.3	34.4	33.4	32.5	31.5	30.6
0.5	48.0	47.1	46.2	45.4	44.5	43.6	42.7	41.8	40.9	39.9
0.4	56.4	55.6	54.8	53.9	53.1	52.3	51.4	50.6	49.7	48.9
0.3	64.2	63.4	62.7	61.9	61.1	60.4	59.6	58.8	58.0	57.2
0.2	71.2	70.5	69.8	69.1	68.5	67.8	67.1	66.3	65.6	64.9
0.1	77.4	76.8	76.2	75.6	75.0	74.4	73.8	73.1	72.5	71.8
0.0	82.8	82.3	81.8	81.2	80.7	80.2	79.6	79.1	78.5	78.0
−0.0	82.8	83.3	83.7	84.2	84.7	85.1	85.6	86.0	86.5	86.9
−0.1	87.3	87.7	88.1	88.5	88.9	89.3	89.6	90.0	90.3	90.7
−0.2	91.0	91.3	91.6	92.0	92.3	92.6	92.8	93.1	93.4	93.7
−0.3	93.9	94.2	94.4	94.6	94.9	95.1	95.3	95.5	95.7	95.9
−0.4	96.1	96.3	96.4	96.6	96.8	96.9	97.1	97.2	97.4	97.5
−0.5	97.6	97.7	97.9	98.0	98.1	98.2	98.3	98.4	98.4	98.5
−0.6	98.6	98.7	98.7	98.8	98.9	98.9	99.0	99.0	99.1	99.1
−0.7	99.2	99.2	99.2	99.3	99.3	99.3	99.3	99.4	99.4	99.4
−0.8	99.4	99.4	99.4	99.4	99.5	99.5	99.5	99.5	99.5	99.5
−0.9	99.5	99.5	99.5	99.5	99.5	99.5	99.5	99.5	99.5	99.5
−1.0	99.5

b	0	1	2	3	4	5	6	7	8	9
1.0	0.0
0.9	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
0.8	0.1	0.1	0.1	0.1	0.0	0.0	0.0	0.0	0.0	0.0
0.7	0.4	0.3	0.3	0.3	0.2	0.2	0.2	0.2	0.1	0.1
0.6	1.0	0.9	0.8	0.8	0.7	0.6	0.6	0.5	0.5	0.4
0.5	2.0	1.9	1.8	1.6	1.5	1.4	1.3	1.2	1.1	1.1
0.4	3.6	3.4	3.2	3.1	2.9	2.7	2.6	2.4	2.3	2.1
0.3	5.8	5.6	5.3	5.1	4.9	4.6	4.4	4.2	4.0	3.8
0.2	8.8	8.5	8.2	7.9	7.5	7.2	6.9	6.7	6.4	6.1
0.1	12.6	12.2	11.8	11.4	11.0	10.6	10.2	9.9	9.5	9.2
0.0	17.2	16.7	16.2	15.8	15.3	14.8	14.4	13.9	13.5	13.0
−0.0	17.2	17.7	18.3	18.8	19.3	19.9	20.4	21.0	21.5	22.1
−0.1	22.7	23.3	23.9	24.5	25.1	25.7	26.4	27.0	27.7	28.3
−0.2	29.0	29.7	30.4	31.0	31.7	32.4	33.2	33.9	34.6	35.3
−0.3	36.1	36.8	37.6	38.4	39.1	39.9	40.7	41.5	42.3	43.1
−0.4	43.9	44.7	45.6	46.4	47.2	48.1	48.9	49.8	50.6	51.5
−0.5	52.4	53.3	54.1	55.0	55.9	56.8	57.7	58.6	59.6	60.5
−0.6	61.4	62.3	63.3	64.2	65.1	66.1	67.0	68.0	68.9	69.9
−0.7	70.8	71.8	72.8	73.7	74.7	75.7	76.7	77.6	78.6	79.6
−0.8	80.6	81.6	82.6	83.6	84.5	85.5	86.5	87.5	88.5	89.5
−0.9	90.5	91.5	92.5	93.5	94.5	95.5	96.5	97.5	98.5	99.5
−1.0	100.0

b	0	1	2	3	4	5	6	7	8	9
1.0	0.0
0.9	10.0	9.0	8.0	7.0	6.0	5.0	4.0	3.0	2.0	1.0
0.8	19.9	18.9	17.9	16.9	16.0	15.0	14.0	13.0	12.0	11.0
0.7	29.6	28.7	27.7	26.7	25.8	24.8	23.8	22.8	21.9	20.9
0.6	39.0	38.1	37.2	36.2	35.3	34.4	33.4	32.5	31.5	30.6
0.5	48.0	47.1	46.2	45.4	44.5	43.6	42.7	41.8	40.9	39.9
0.4	56.4	55.6	54.8	53.9	53.1	52.3	51.4	50.6	49.7	48.9
0.3	64.2	63.4	62.7	61.9	61.1	60.4	59.6	58.8	58.0	57.2
0.2	71.2	70.5	69.8	69.1	68.5	67.8	67.1	66.3	65.6	64.9
0.1	77.4	76.8	76.2	75.6	75.0	74.4	73.8	73.1	72.5	71.8
0.0	82.8	82.3	81.8	81.2	80.7	80.2	79.6	79.1	78.5	78.0
−0.0	82.8	83.3	83.7	84.2	84.7	85.1	85.6	86.0	86.5	86.9
−0.1	87.3	87.7	88.1	88.5	88.9	89.3	89.6	90.0	90.3	90.7
−0.2	91.0	91.3	91.6	92.0	92.3	92.6	92.8	93.1	93.4	93.7
−0.3	93.9	94.2	94.4	94.6	94.9	95.1	95.3	95.5	95.7	95.9
−0.4	96.1	96.3	96.4	96.6	96.8	96.9	97.1	97.2	97.4	97.5
−0.5	97.6	97.7	97.9	98.0	98.1	98.2	98.3	98.4	98.4	98.5
−0.6	98.6	98.7	98.7	98.8	98.9	98.9	99.0	99.0	99.1	99.1
−0.7	99.2	99.2	99.2	99.3	99.3	99.3	99.3	99.4	99.4	99.4
−0.8	99.4	99.4	99.4	99.4	99.5	99.5	99.5	99.5	99.5	99.5
−0.9	99.5	99.5	99.5	99.5	99.5	99.5	99.5	99.5	99.5	99.5
−1.0	99.5

b	0	1	2	3	4	5	6	7	8	9
1.0	0.0
0.9	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
0.8	0.1	0.1	0.1	0.1	0.0	0.0	0.0	0.0	0.0	0.0
0.7	0.4	0.3	0.3	0.3	0.2	0.2	0.2	0.2	0.1	0.1
0.6	1.0	0.9	0.8	0.8	0.7	0.6	0.6	0.5	0.5	0.4
0.5	2.0	1.9	1.8	1.6	1.5	1.4	1.3	1.2	1.1	1.1
0.4	3.6	3.4	3.2	3.1	2.9	2.7	2.6	2.4	2.3	2.1
0.3	5.8	5.6	5.3	5.1	4.9	4.6	4.4	4.2	4.0	3.8
0.2	8.8	8.5	8.2	7.9	7.5	7.2	6.9	6.7	6.4	6.1
0.1	12.6	12.2	11.8	11.4	11.0	10.6	10.2	9.9	9.5	9.2
0.0	17.2	16.7	16.2	15.8	15.3	14.8	14.4	13.9	13.5	13.0
−0.0	17.2	17.7	18.3	18.8	19.3	19.9	20.4	21.0	21.5	22.1
−0.1	22.7	23.3	23.9	24.5	25.1	25.7	26.4	27.0	27.7	28.3
−0.2	29.0	29.7	30.4	31.0	31.7	32.4	33.2	33.9	34.6	35.3
−0.3	36.1	36.8	37.6	38.4	39.1	39.9	40.7	41.5	42.3	43.1
−0.4	43.9	44.7	45.6	46.4	47.2	48.1	48.9	49.8	50.6	51.5
−0.5	52.4	53.3	54.1	55.0	55.9	56.8	57.7	58.6	59.6	60.5
−0.6	61.4	62.3	63.3	64.2	65.1	66.1	67.0	68.0	68.9	69.9
−0.7	70.8	71.8	72.8	73.7	74.7	75.7	76.7	77.6	78.6	79.6
−0.8	80.6	81.6	82.6	83.6	84.5	85.5	86.5	87.5	88.5	89.5
−0.9	90.5	91.5	92.5	93.5	94.5	95.5	96.5	97.5	98.5	99.5
−1.0	100.0

Abstract

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Figures (4)

Tables (2)

Equations (19)

Journal of the Optical Society of America