INSTITUTE OF PHYSICS PUBLISHING METROLOGIA Metrologia 40 (2003) S81–S84 PII: S0026-1394(03)56067-4 Stray-light correction algorithm for spectrographs Steven W Brown 1 , B Carol Johnson 1 , Michael E Feinholz 2 , Mark A Yarbrough 2 , Stephanie J Flora 2 , Keith R Lykke 1 and Dennis K Clark 3 1 National Institute of Standards and Technology, Gaithersburg, MD 20899, USA 2 Moss Landing Marine Laboratories, Moss Landing, CA 95039, USA 3 National Oceanic and Atmospheric Administration, National Environmental Satellite Data and Information Service, Camp Springs, MD 20746, USA E-mail: swbrown@nist.gov Published 7 February 2003 Online at stacks.iop.org/Met/40/S81 Abstract In this paper, we describe an algorithm to correct a spectrograph’s response for stray light. Two recursion relations are developed: one to correct the system response when measuring broad-band calibration sources, and a second to correct the response when measuring sources of unknown radiance. The algorithm requires a detailed understanding of the effect of stray light in the spectrograph on the instrument’s response. Using tunable laser sources, a dual spectrograph instrument designed to measure the up-welling radiance in the ocean was characterized for stray light. A stray-light correction algorithm was developed, based on the results of these measurements. The instrument’s response was corrected for stray light, and the effects on measured up-welling in-water radiance were evaluated. 1. Introduction Spectrographs are dispersive instruments with multi-element detectors that enable simultaneous acquisition of an entire spectrum over some finite spectral width. With the rapid improvements in detector-array technologies, spectrographs are now being used in a variety of commercial and scientific applications. There are intrinsic limitations in the background signal originating from radiation scattered from imperfections in the grating and other optical elements. This unwanted background radiation, called stray light, while small—of the order of 0.01% or less of the incident spectral radiance in a single grating spectrograph—can give rise to unforeseen errors, often much larger than anticipated, when the spectral distribution of a source being measured differs significantly from the spectral distribution of the calibration source. This is a situation routinely encountered in oceanographic measurements, for example, where instruments are calibrated against incandescent sources with a peak radiance in the short- wave infrared and subsequently used to measure the radiance of the ocean, which peaks in the blue spectral region. In this paper, we describe a recursion relation to correct a spectrograph’s responsivity and an unknown source’s radiance for effects of stray light. Using tunable, narrow-band laser sources available on the newly developed facility for Spectral Irradiance and Radiance responsivity Calibrations using Uniform Sources (SIRCUS) at the National Institute of Standards and Technology [1], a spectrograph can be fully characterized for stray light, and model parameters for the stray-light correction algorithm can be developed [2]. As an example, results from the characterization and stray-light correction of a dual CCD spectrograph, the Marine Optical System (MOS), are presented. 2. Stray-light correction algorithm In general, the total signal from element i of a CCD or diode array spectrograph is given by the equation: S i =  r i (λ)L(λ) dλ, (1) where r i (λ) is the spectral responsivity of element i and L(λ) is the spectral radiance of the source being measured. Note that r i (λ) is the spectral responsivity of element i when considered as part of the spectrograph and includes effects such as grating efficiency and mirror losses. For monochromatic radiation, the entrance slit is spatially imaged on the detector. The image 0026-1394/03/SS0081+04$30.00 © 2003 BIPM and IOP Publishing Ltd Printed in the UK S81