## Abstract

Derivative spectrophotometry is a relatively new way of photometric measurements that was suggested by French and others. We classify the methods of derivative spectrophotometry into two main classes. In one we place those instruments in which the derivative is produced by operations on light beams in the optical part of the spectrophotometer. In the other class we place those instruments in which the derivative is obtained by operation on the output signal of a conventional spectrophotometer. After comparison of two simplified systems, each representing one of the two classes, we find that there is no significant difference with respect to signal-to-noise ratio between the two classes. When applications are considered, instruments of the first class are found to be preferable for certain biological and biochemical research work.

© 1965 Optical Society of America

Full Article |

PDF Article
### Equations (8)

Equations on this page are rendered with MathJax. Learn more.

(1)
$$\mathrm{\Delta}V(\mathrm{\lambda})=V({\mathrm{\lambda}}_{2})-V({\mathrm{\lambda}}_{1}),$$
(2)
$$\begin{array}{ll}\mathrm{\Delta}V(\mathrm{\lambda})\hfill & =R\{[I({\mathrm{\lambda}}_{1})+{i}_{1}]-[I({\mathrm{\lambda}}_{2})+{i}_{2}]\}\hfill \\ \hfill & =R({I}_{1}-{I}_{2})+R({i}_{1}-{i}_{2}),\hfill \end{array}$$
(3)
$${[{\u3008{n}^{2}\u3009}_{\text{av}}]}^{\frac{1}{2}}={(e\mathrm{\Delta}fR)}^{\frac{1}{2}}{(2{G}^{2}IR)}^{\frac{1}{2}},$$
(4)
$${\u3008{N}^{2}\u3009}_{\text{av}}={\u3008{{n}_{1}}^{2}\u3009}_{\text{av}}+{\u3008{{n}_{2}}^{2}\u3009}_{\text{av}}=(2e\mathrm{\Delta}f{G}^{2}{R}^{2})({I}_{1}+{I}_{2}).$$
(5)
$${[{\u3008{N}^{2}\u3009}_{\text{av}}]}^{\frac{1}{2}}={(2e\mathrm{\Delta}f{G}^{2}{R}^{2})}^{\frac{1}{2}}{({I}_{1}+{I}_{2})}^{\frac{1}{2}}.$$
(6)
$$S=R({I}_{1}-{I}_{2}),$$
(7)
$$(\text{SNR})=S/{[{\u3008{N}^{2}\u3009}_{\text{av}}]}^{\frac{1}{2}}=({I}_{1}-{I}_{2})/[{(2e\mathrm{\Delta}f{G}^{2})}^{\frac{1}{2}}{({I}_{1}+{I}_{2})}^{\frac{1}{2}}].$$
(8)
$$F={(\text{SNR})}_{\text{D}}/{(\text{SNR})}_{\text{T}}=\sqrt{2},$$