Download Heterodyne Laser Metrology System: Measuring Position using Zero-Crossings and more Lab Reports Electrical and Electronics Engineering in PDF only on Docsity! EE 521 Measurement and Instrumentation Fall 2006 - Dr. Anders M. Jorgensen Heterodyne Laser Metrology System In this project you will use a laser metrology system to measure the position of a piezo- electric positioning device which, nominally, is tracing out a triangular waveform at a nominal frequency of 500 Hz and a nominal amplitude of a few micrometers. Background: The Navy Prototype Optical Interferometer (NPOI) is located in Flagstaff, AZ. It measures approximately 400 m in diameter, which allows it to obtain a angular resolution in the sky at visible wavelengths (∼ 500 nm) of approximately λ D = 500 nm 400 m = 10−9 radians = 0.3 mas One milliarcsecond (mas) is approximately 3 × 10−7 ◦ . By comparison, the resolution of the human eye is approximately 3 arcminutes, or 0.05◦. The extremely high resolution of optical interferometers is necessary because stars have very small angular diameters. An interfer- ometer works by collecting light at telescope pairs, transmitting it to a central location and 1 interfering the two beams. The intensity of the combined beam depends on the relative phase of the two beams, and varies periodically with phase difference, completing a full sinusoid as the phase is changed by 2π, or equivalently as the relative paths are changed by one wavelength. We are really interested in the amplitude of this periodic signal, so we delay one beam in a periodic pattern which when plotted as a function of time looks like a triangular pattern. When one of the beams is delayed in this pattern, the intensity of the combined beam will vary sinusoidally with time at the detector. At the NPOI the amplitude of this triangular variation is a few microns and its period 2 ms. The motion is created by a stack of piezo- electric elements which are driven by a triangular high-voltage wave. In order to verify that the piezo really does trace out the triangular pattern that we expect we use a two-frequency heterodyne interferometer. The setup at NPOI is very similar to that described in section 7.3.3.2.3 and Figure 7.52 of Northrop (pages 419-421). Assignment: Use the given metrology data to compute the position of a piezo-electric stack as a function of time. Read Northrop section 7.3.3.2. Each of the frequencies at ω1 and ω2 are waves that propagate according to E1 = E1o cos (ω1t − k1x) and E2 = E1o cos (ω2t − k2x) At the NPOI the two frequencies are produced from a HeNe laser by passing the laser beam through an acousto-optical modulator (AOM). The two frequencies emerging from the AOM are separated by 2 MHz. 1. Derive expressions for the voltages produces by PD1, R(t), and PD2, M(t). Note that the photodiodes act as low-pass filters and smooth out the high frequency components above 100 MHz. Simplify the expressions by replacing constant terms with a constant. 2. Show that the reference signal has constant period. Write a program which computes the times of positive zero-crossings in the reference signal. Then compute the mean and standard deviation of the time between successive positive zero-crossings. Notice that the signals have been high-pass filtered, eliminating the DC component. This means that we conveniently use the zero-crossings as time markers (We could choose any other DC level as our reference level for crossings if we wanted to. However, a level near the middle of the amplitude range gives the best SNR). The signal is very stable so that the variability is due to the digitization and discrete time measurements. The width of this peak determines the accuracy with which you can determine zero-crossings. 3. Create a list of positive zero-crossings in the measuring signal. Use the same procedure that you used to find the positive zero-crossings in the reference signal. You may want to save this data set as a file. 4. Compute the average speed of RR1. The average time between zero-crossings in the measuring signal can be used to measure the average speed of RR1. 2
