Home

Light Transport in Tissue

The Boundary Condition Parameter in the Presence of a Glass Slide

When a glass slide is present at the boundary then the reflection moments R₁ and R₂ must be calculated using the method outlined in Section B.3. This means that the parameter A is a function of two variables--the ratio of the index of refraction of the medium to that of the environment and the ratio of the index of refraction of the glass slide to the environment. Since the index of refraction of glass and quartz varies between 1.40 and 1.60, values in this limited range are presented in Table B.7.

Polynomial approximations for the tabulated values of A in Table B.7 are

A^1.00(n)=-0.13755 n³+4.33904 n²-4.90466 n+1.68960 (B52)

A^1.40(n)=-0.40853 n³+5.17127 n²-6.33960 n+2.80840 (B53)

A^1.45(n)=-0.41535 n³+5.16138 n²-6.27852 n+2.79732 (B54)

A^1.50(n)=-0.42592 n³+5.17218 n²-6.24603 n+2.79862 (B55)

A^1.55(n)=-0.43239 n³+5.16867 n²-6.19220 n+2.78879 (B56)

A^1.60(n)=-0.44400 n³+5.19174 n²-6.17761 n+2.79812 (B57)

These values are compared with the exact values in Table B.8. If indices of refraction of glass are required then it is necessary to interpolate between values given by Equations (B.53)-(B.57).

Table B.7: Values of A for various indicies of refraction. Light is incident from a medium (n_i), passes through glass (n_g), and transmitted into another medium (n_t). The superscripts indicate n_g/n_t.

ni/nt	A1.00	A1.40	A1.45	A1.50	A1.55	A1.60
1.00	1.000	1.253	1.286	1.320	1.354	1.389
1.10	1.353	1.535	1.570	1.606	1.643	1.681
1.20	1.810	1.935	1.971	2.009	2.047	2.087
1.30	2.346	2.411	2.448	2.486	2.526	2.568
1.40	2.955	2.955	2.991	3.030	3.071	3.114
1.50	3.636	3.562	3.597	3.636	3.677	3.721
1.60	4.388	4.232	4.266	4.303	4.344	4.388
1.70	5.213	4.966	4.996	5.032	5.072	5.116
1.80	6.113	5.763	5.790	5.823	5.861	5.904
1.90	7.089	6.626	6.648	6.678	6.713	6.754

Table B.8: Differences between of polynomial approximations for A and the exact values. See caption for Table B.7 for details.

ni/nt	$\Delta A^{1.00}$	$\Delta A^{1.40}$	$\Delta A^{1.45}$	$\Delta A^{1.50}$	$\Delta A^{1.55}$	$\Delta A^{1.60}$
1.00	0.014	0.021	0.021	0.021	0.021	0.021
1.10	-0.009	-0.013	-0.013	-0.013	-0.013	-0.013
1.20	-0.005	-0.007	-0.007	-0.006	-0.007	-0.007
1.30	0.002	0.002	0.003	0.002	0.002	0.002
1.40	0.005	0.007	0.007	0.007	0.007	0.007
1.50	0.005	0.006	0.006	0.007	0.006	0.006
1.60	0.001	0.002	0.002	0.002	0.002	0.002
1.70	-0.003	-0.003	-0.004	-0.003	-0.003	-0.003
1.80	-0.005	-0.007	-0.007	-0.007	-0.007	-0.006
1.90	-0.002	-0.003	-0.004	-0.003	-0.004	-0.003

S. A. Prahl."Light Transport in Tissue," PhD thesis, University of Texas at Austin, 1988.