StrayLightP - Stray light curve correction

J E Patterson - jepspectro.com - 20231119

Description

Spectrophotometers have some stray light or detector dark current which causes the calibration to be non linear at high absorbances.

Absorbance = Log (Incident light Intensity)/(Transmitted light Intensity).

This program corrects for the calibration curvature caused by the presence of stray light.

Absorbance A = log(Io/I) .... ideal
Io is the incident light intensity and I is the transmitted light intensity.
A' = log(Io+Is)/(I+Is) .... measured absorbance
Is is the stray light intensity (or the dark current in the detector)
A = A'-log(k(1-10^A')+1 ....................................................... (1)
where k = Is/Io and 100k = % stray light
k = (10^(A'-A)-1)/(1-10^A')
C1 and C2 are standards and A1' and A2' are the measured absorbances.
k2 = (10^(A2'-A2)-1)/(1-10^A2') ............................................... (2)
Substituting A1 in equation (1)
A1 = A1'-log(k1(1-10^A1')+1)
For ideal absorbances A2 = A1(C2/C1)
A2 = (A1'-log(k1((1-10^A1')+1)C2/C1 ................................ (3)

Equation (3) can be substituted in equation (2) and an iteration runs until (k1 - k2)*100 = 0 within an error tolerance determined by the FIX, SCI or ENG significant digits setting.
The value for k is now set equal to k1, the last value calculated.
100k = % stray light

You can enter f USER to avoid the f or GSB key during data input.

Input two standard concentration values C1 ENTER C2 GSB A.
Input two corresponding absorbances A1' ENTER A2' GSB B.
The % stray light is displayed. This is stored in register 8.

Input an unknown sample absorbance A' GSB D the resulting concentration C' is displayed and stored in register 9

Example 1:
Standard data: (Concentrations C1, C2 = 5, 10, Absorbances A1', A2' = 0.53, 0.83).
5 ENTER
1 0 GSB A
. 5 3 ENTER
. 8 7 GSB B
Stray light is 9.62%

This curvature is not unusual for Atomic Absorption spectrometry. Spectrophotometry can be much more linear in the near absence of stray light.

Example 2:
Unknown sample absorbance is 0.74
. 7 4 GSB C
The unknown sample concentration is 7.66 units, using the same concentration units as the standards.
Repeat A' GSB C for further samples.

Program Resources

Labels

Name	Description
A	C1 Enter C2 GSB A, Enter concentrations
B	A1' Enter A2' GSB B, Enter measured absorbances
C	Enter sample absorbance GSB A' = concentration C'
1	Start of loop

Storage Registers

Name	Description	Name	Description
1	C1 concentration of standard 1	8	% stray light
2	C2 concentration of standard 2	9	Concentration C'
4	Stray light fraction	.1	A1' absorbance of standard 1
5	Stray light old	.2	A2' absorbance of standard 2
6	Temp 1	.3	A' sample absorbance
7	Temp 2	I	Loop counter register, decrement 20 to 0.

Program

Line	Display	Key Sequence	Line	Display	Key Sequence	Line	Display	Key Sequence
000			027	43 13	g LOG	054	43,30, 0	g TEST x≠0
001	42,21,11	f LBL A	028	30	−	055	22 1	GTO 1
002	44 2	STO 2	029	44 6	STO 6	056	45 4	RCL 4
003	33	R⬇	030	45 2	RCL 2	057	26	EEX
004	44 1	STO 1	031	45 1	RCL 1	058	2	2
005	43 32	g RTN	032	10	÷	059	20	×
006	42,21,12	f LBL B	033	20	×	060	44 8	STO 8
007	44 .2	STO . 2	034	44 7	STO 7	061	43 32	g RTN
008	33	R⬇	035	45 .2	RCL . 2	062	42,21,13	f LBL C
009	44 .1	STO . 1	036	45 7	RCL 7	063	44 .3	STO . 3
010	2	2	037	30	−	064	1	1
011	0	0	038	13	10ˣ	065	45 .3	RCL . 3
012	44 25	STO I	039	1	1	066	13	10ˣ
013	0	0	040	30	−	067	30	−
014	44 4	STO 4	041	1	1	068	45 4	RCL 4
015	42,21, 1	f LBL 1	042	36	ENTER	069	20	×
016	45 4	RCL 4	043	45 .2	RCL . 2	070	1	1
017	44 5	STO 5	044	13	10ˣ	071	40	+
018	45 .1	RCL . 1	045	30	−	072	43 13	g LOG
019	1	1	046	10	÷	073	30	−
020	45 .1	RCL . 1	047	44 4	STO 4	074	45 6	RCL 6
021	13	10ˣ	048	45 5	RCL 5	075	10	÷
022	30	−	049	30	−	076	45 1	RCL 1
023	45 5	RCL 5	050	26	EEX	077	20	×
024	20	×	051	2	2	078	44 9	STO 9
025	1	1	052	20	×	079	43 32	g RTN
026	40	+	053	43 34	g RND