# Response functions

1. Sep 7, 2009

### natski

1. The problem statement, all variables and given/known data

Consider you are conducting an experiment of using a photometer to measure the radiation from a blackbody source. Write down the expression for the received flux from the blackbody for two different cases:

a) your photometer has a square-response function going from wavelengths $\lambda_1$ to $\lambda_2$ with an efficiency of X.

b) your photometer has an efficiency characterised by the function f(\lambda).

2. Relevant equations

None

3. The attempt at a solution

a) X \cdot \int_{\lambda_1}^{\lambda_2} B(\lambda,T) \, \mathrm{d}\lambda

where B(\lamba,T) is the Planck function

b) \int_{0}^{\infty} B(\lambda,T) \cdot f(\lambda) \, \mathrm{d}\lambda

Is this correct? I am confused as to whether I should be multiplying inside the integrand or doing some kind of convolution in Fourier space or something?

Thanks,

Natski
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution