Infrared Photometry

Introduction
There is no unique way to reduce astronomical photoelectric photometry. If 100 astronomers were polled, they would probably advocate 100 different reduction techniques. The process described here is just one of those methods. It is strongly weighted towards the classical technique presented by Hardie (1962).

Magnitudes represent the intensity of some quantity on a logarithmic, not linear, scale. This basic conversion for completeness is restated as:

where n is the number of counts acquired during and an integration of t seconds. The subscripts refer to measurements of star + sky or sky alone. The resulting value m is a generic quantity that becomes a specific quantity j or h in the remaining discussion. This is also known as the instrumental or raw magnitude.

Despite the simplicity of this calculation, there are several complications that need to be considered. First, for pulse-counting systems, the values for n need to be corrected for dead time prior to insertion in Eqn. 1. A second problem arises if analog instrumentation is used. In this case the recorded number of counts, or possibly an intensity read from a strip-chart recorder, needs to be modified by a scale factor. For the specific case of the Optec SSP-3 or SSP-4 solid state photometers, the number on the 4-digit display or computer display needs to be divided by the scale factor (i.e., either 1, 10, or 100) and the integration time (e.g., 1, 5 or 10 seconds).

Central to the discussion of calibration and data reduction is the idea of not one, but three types of magnitudes: instrumental or raw system, natural system, and standard system magnitudes.

Instrumental or Raw System Magnitudes

Instrumental magnitudes are simply a logarithmic conversion of raw data counts, with appropriate corrections for background light, dead time, scale factor and integration time. Explicitly excluded from these corrections is the removal of the effects of atmospheric extinction and color transformation. The instrumental magnitude scale is totally dependent on the units of measurement for a particular piece of equipment. Instrumental magnitudes are denoted by lowercase letters j and h.

The net J and h band counts are with sky counts removed, normalized for a gain of X1 and gate/integration time of 1 second.

Natural System Magnitudes

Natural system magnitudes are instrumental magnitudes that have been corrected for atmospheric effects. In essence, the natural magnitude scale is the scale that the instrument would possess if the observations were made from space. The photometric characteristics of the natural-system are not invariant, but slowly change with time as filters age, mirror coatings deteriorate, etc. Natural system magnitudes are denoted by jo and ho.

Standard System Magnitudes

Standard system magnitudes are natural-system magnitudes that have been transformed to match a set of specified standard stars. The transformation removes the effects of small differences between an observer's equipment and that originally used to define the set of standards. If the differences are small, a unique and valid transformation can be found. However, if there is a large mismatch between instruments, it is impossible to satisfactorily complete this process. Standard magnitudes are denoted by uppercase letters, J and H.

Two general relationships are defined:

Qi, Qn, and Qs are the instrumental, natural system, and standard system magnitudes of a particular photometric quantity. This quantity can represent a measurement through a single filter (i.e., a simple magnitude), the ratio of measurements through two filters (i.e., a simple color index), or a combination of measurements through three of more filters (i.e., a complex index).

Eqn. 4 and 5 are equivalent to mo = m - k X and removes the effects of atmospheric extinction and transform the data to the standard system.

The J H system defined here uses one simple magnitude, J, and one simple color indice, (J-H). Specific forms of the above equations used in J H photometry are as follows:

Eqn. 4 expands to the set of equations for the natural system magnitudes:

Present Page Version as of 1 November 2006

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