Michelson Lab.pdf

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You are interested in looking at the graph of amplitude vs. wavelength at the expectedwavelength of the HeNe laser. Sometimes the graph does not show the desired range.Use the input fields – Max Wavelength, and Min Wavelength to alter the range that isbeing viewed. Note that the view is in units of meters. The screen image can becaptured by pressing Alt-PrntScrn (the alternate key and the print screen key).8 of 13
Appendix 2 – Mathematics of Fourier Transform SpectroscopyIntroduction:The first thing we are interested in is the expected power output of the detector givena monochromatic input source. From here it is easy to generalize to the morephysically realistic case of a continuous input source. The next step is themathematics of the Fourier Transform itself, which allows us to determine thespectrum of the source given the value of the modulated power output at the detector.Finally, returning to the idealized monochromatic source we use a clevermathematical trick to obtain the spectral resolution of the interferometer setup.Section 1: Derivation of Expected Power OutputBefore we begin with the math let’s quickly go over the experimental setup. The beamenters the interferometer at the input and travels to the beam splitter. At the beamsplitter, a fraction of the beam is reflected toward Mirror 1 and the remaining fractionis transmitted toward Mirror 2. The beam which was previously reflected by the BS(the one which travelled along Z1) is now transmitted and the part of the beam whichwas originally transmitted is now reflected. The result is that the two components ofthe beam exit through the output port.But why is this at all useful? Let’s start with the case in which path Z1 is equal to pathZ2. In that case, the two beams travelling along their respective paths will be in phasewith each other at the output port and will therefore constructively interfere. If, on theother hand, the two paths differ by half a wavelength, the two beams will be out ofphase with each other and will destructively interfere. The trick of the FourierTransform Spectrometer is that one path (let’s say Z1) is held constant while the otherpath (Z2) is varied. By observing how the intensity at the output port varies with thepath difference we can effectively deduce the spectrum of the source. This isaccomplished by a clever mathematical device known as the Fourier Transform.Now for the maths. Let’s assume for simplicity that the input is a monochromaticsource; later we’ll generalize this result to the more physically realistic case of acontinuous input spectrum. Our input source has the form: A sin kztE MS09 of 13
Page 4 and 5: Part (D) Measuring the wavelength a
Page 6 and 7: Additional Notes: A good speed will
Page 10 and 11: The beam enters through the input p
Page 12 and 13: Section 3: Calculation of Spectral

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