Theoretical impulse response and its normalization

[omg!]

greetings, helpful people around the world,

we all have heard once in our lives that the signal that is measure from your instrument, be it a spectrometer, optical microscope or an NMR machine, is not the real signal distribution, but the convolution of the real signal with an instrument function, sometimes called impulse response, resolution function, or who knows what.

my (first) question concerns the absolute scaling of the impulse response. is it a normalized function? if you had an instrument with a tunable impulse response, say an optical microscope with a tunable objective numerical aperture, how does the impusel response change as numerical aperture is varied? the width of the function obviously will vary, but what happens with its amplitude?

thank you all!

 

[eljose79]

Dear poster,

Thank you for bringing up an important topic in the field of instrumentation. You are correct in stating that the signal measured from an instrument is not the exact representation of the sample being studied, but rather a convolution of the real signal with the instrument function. This is a crucial concept to understand in order to accurately interpret and analyze data obtained from instruments.

To answer your first question, the absolute scaling of the impulse response depends on the specific instrument being used. In general, the impulse response is a normalized function, meaning that its amplitude is scaled to a maximum value of 1. This allows for a consistent comparison between different instruments and their respective impulse responses.

In regards to your second question, the impulse response does change as the numerical aperture is varied in an optical microscope. As you mentioned, the width of the function will vary, but the amplitude will also change. As the numerical aperture is increased, the amplitude of the impulse response will decrease. This is because a higher numerical aperture allows for more light to be collected, resulting in a stronger signal and a narrower impulse response.

I hope this answers your questions. Keep exploring and questioning in the world of science!