Difference and relationship between spectrometers and interferometers

[wassup_g]

Q1. A spectrometer measures the optical power spectral density as a function of the wavelength or optical frequency (say F(v) v.s. v, where "v" is frequency), is this right?

Q2. An interferometer can be used to detect the amplitude of a light source v.s. the path difference (x), i.e. if the detected signal is f(x), then we can plot f as a function of the path difference. Can it be used to detect a signal which is as a function of time, i.e. am I able to plot f(t) against time using results obtained from an interferometer?

Q3. Assume a laser light source is sent to both a spectometer and an interferometer, then what is the relationship between the signal obtained using the interferometer (in time domain, i.e. f(t) or f(x) mentioned in Q2) and the signal obtained using the spectrometer (i.e. the spectrum or F(v) mentioned in Q1)?

For Q3, personally I don't think F(v) and f(t) are Fourier transform pairs because they must both be real signals, I wonder if the answer of Q3 is about Hilbert transform.

 

[Valerie Park]

A1. Yes, a spectrometer measures the optical power spectral density as a function of the wavelength or optical frequency.A2. Yes, an interferometer can be used to detect a signal which is as a function of time. By calculating the phase difference between two waves and then correlating the phase difference with the time difference, one can plot f(t) against time using results obtained from an interferometer.A3. The relationship between the signal obtained using the interferometer and the signal obtained using the spectrometer depends on the type of measurement being taken. If the measurement is of the frequency spectrum, then the relationship is that the signal obtained using the interferometer can be used to calculate the Fourier transform of the signal obtained using the spectrometer. If the measurement is of the time domain, then the relationship is that the signal obtained using the spectrometer can be used to calculate the inverse Fourier transform of the signal obtained using the interferometer.