## Abstract

We present the improved structure and operating principle of a spectrophotometric mean that allows us for the recording of the transmittance of a thin-film filter over an ultra-wide range of optical densities (from 0 to 11) between 400 and 1000 nm. The operation of this apparatus is based on the combined use of a high power supercontinuum laser source, a tunable volume hologram filter, a standard monochromator and a scientific grade CCD camera. The experimentally recorded noise floor is in good accordance with the optical density values given by the theoretical approach. A demonstration of the sensitivity gain provided by this new set-up with respect to standard spectrophotometric means is performed via the characterization of various types of filters (band-pass, long-pass, short-pass, and notch).

© 2015 Optical Society of America

Full Article |

PDF Article

**OSA Recommended Articles**
### Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.

### Equations (16)

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

(1)
$$F(\lambda )={10}^{\text{OD}(\lambda )}\frac{{S}_{C}}{{S}_{R}}(\lambda )$$
(2)
$${S}_{T}=0.7\times {2}^{16}\times N\approx 45000\times N$$
(3)
$${T}_{F}(\lambda )=\frac{{F}_{\text{TFF}}(\lambda )}{{F}_{\text{BL}}(\lambda )}$$
(4)
$$\overline{m}={\overline{m}}_{\text{DC}}+{\eta}_{C}(\lambda )\frac{\alpha (\lambda ){T}_{\mathrm{F}}(\lambda )\times {10}^{-\text{OD}(\lambda )}P(\lambda )}{Nh\nu}{\tau}_{\lambda}={\overline{m}}_{\text{DC}}+{\overline{m}}_{\lambda}$$
(5)
$$M={2}^{16}\frac{\overline{m}}{\text{FWC}}+{M}_{0}$$
(6)
$${S}_{C}=\{\begin{array}{ll}{S}_{T}\hfill & \text{for}{T}_{F}\ge {T}_{c}\hfill \\ {S}_{T}\frac{{T}_{F}}{{T}_{c}}\hfill & \text{for}{T}_{F}<{T}_{c}\hfill \end{array}$$
(7)
$${T}_{c}(\lambda )=\frac{{[{\tau}_{\lambda}]}_{\text{BL}}}{100}{10}^{-{[OD]}_{\text{BL}}}$$
(8)
$${\sigma}_{m}^{2}=\overline{m}+{I}_{\text{DC}}{\tau}_{\lambda}+{\sigma}_{\text{RN}}^{2}=\overline{m}+{\sigma}_{0}^{2}$$
(9)
$${\sigma}_{{S}_{C}}^{2}={\left(\frac{{2}^{16}}{\text{FWC}}\right)}^{2}[N\overline{m}+{N}_{c}{\sigma}_{0}^{2}]$$
(10)
$$\begin{array}{l}\text{FWC}=100000\phantom{\rule{0.2em}{0ex}}{\mathrm{e}}^{-}\\ {I}_{\text{DC}}=0.001\phantom{\rule{0.2em}{0ex}}{\mathrm{e}}^{-}/\mathrm{s}@\phantom{\rule{0.2em}{0ex}}-70\phantom{\rule{0.2em}{0ex}}\xb0\text{Coperation}\\ {\mathrm{\sigma}}_{\text{RN}}=9\phantom{\rule{0.2em}{0ex}}{\mathrm{e}}^{-}\text{rms}@\phantom{\rule{0.2em}{0ex}}2-\text{MHzdigitization}\end{array}$$
(10)
$${\text{SNR}}_{\mathrm{C}}=\frac{{S}_{C}}{{\sigma}_{{S}_{C}}}=\frac{N\times 0.7\text{FWC}\frac{{S}_{c}}{{S}_{T}}}{\sqrt{N\times 0.7\text{FWC}\frac{{S}_{C}}{{S}_{T}}+{N}_{c}{\sigma}_{\text{RN}}^{2}}}$$
(11)
$$V=\frac{G}{S}[{I}_{\text{DC}}+S\beta (\lambda )P(\lambda )]=\frac{G}{S}[{I}_{\text{DC}}+{I}_{\lambda}]\phantom{\rule{1em}{0ex}}\text{with}\phantom{\rule{1em}{0ex}}S=\frac{e{\eta}_{R}(\lambda )}{h\nu}$$
(12)
$${\sigma}_{V}^{2}={\left(\frac{G}{S}\right)}^{2}{\sigma}_{I}^{2}={\left(\frac{G}{S}\right)}^{2}[{S}^{2}{\text{NEP}}^{2}B+2e{I}_{\lambda}B]={G}^{2}[{\text{NEP}}^{2}+\frac{2e\beta (\lambda )P(\lambda )}{S}]B$$
(13)
$${S}_{R}=f{\tau}_{\lambda}\frac{G{I}_{\lambda}}{S}=f{\tau}_{\lambda}G\beta (\lambda )P(\lambda )$$
(14)
$${\sigma}_{{S}_{R}}^{2}={G}^{2}f\left[({\tau}_{\lambda}+0.2){\text{NEP}}^{2}+{\tau}_{\lambda}\frac{2e\beta (\lambda )P(\lambda )}{S}\right]B$$
(15)
$${\text{SNR}}_{R}=\frac{\sqrt{f}{\tau}_{\lambda}\beta (\lambda )P(\lambda )}{\sqrt{B}\sqrt{({\tau}_{\lambda}+0.2){\text{NEP}}^{2}+{\tau}_{\lambda}\frac{2e\beta (\lambda )P(\lambda )}{S}}}$$