Rice University's ELEC 332: In the Lab makes the model experimentally testable. Preparation resets the spectrum analyzer and observes an unmodulated generator output on it and an oscilloscope. A Wavetek function generator supplies external modulation. The specified carrier and message separate three peaks. Marker readouts give frequency and level; narrowing resolution bandwidth shows how the instrument broadens a line.[ref]
Part 3 uses an SA602 analog multiplier module. The message generator also triggers the oscilloscope; multiplier output feeds both displays. A no-offset module supplies a suppressed-carrier control. Replacing it with the offset-adding module restores the carrier; varying levels tests signal distortion. Finally a radio receives the conventional AM transmission, and varying message frequency checks that the heard tone belongs to this source. These are prescribed observations, not reported measurements.[ref]
Calibration matters: verify generator voltage at the connected input, distinguish peak from peak-to-peak amplitude and root mean square, and check analyser units and loading before comparing heights with or power with . The unmodulated carrier is a reference control. Limited resolution can merge sidebands; generator harmonics can add peaks. Rice explicitly demonstrates both limitations in Part 1.[ref]
A complementary University of Kansas procedure, A.2 - Amplitude Modulation, calibrates the added carrier and the suppressed-carrier product separately to peak-to-peak before recombining them. It holds the carrier fixed, varies modulation depth, reads envelope extrema and carrier-to-sideband power differences, then connects the demodulator and adjusts its tunable low-pass filter for recovery, comparing the output with the message. These are setup targets and comparison instructions, not measured results.[ref]
The inference combines time and frequency spectrum readouts: correct sideband spacing tests frequency translation, relative heights test modulation depth, and the recovered message tests the detector. Hardware clipping, receiver filtering and noise can spoil recovery even at . Conversely failure of an envelope detector at does not demonstrate failure of a synchronized multiplier receiver. The two diagrams above illustrate the stipulated linear model only.
Analog multiplier Created 2026-10-14 Updated 2026-10-18
Stellar intensity interferometry measures a star's angular diameter by comparing fluctuations of detected light intensity at separated collectors. Each collector has its own photodetector; an analog multiplier or a digital correlator compares the electrical outputs. Changing the interferometric baseline changes the sampled spatial optical coherence. An unresolved star produces correlated fluctuations; a resolved extended source supplies different mixtures of emission directions, reducing their correlation.
This makes a useful telescope out of a surprising observable: the fluctuations discarded by an ordinary average-brightness measurement. Optical beams need not travel to a common combiner. A relative wave phase perturbation leaves unchanged, so pure phase errors do not directly change the local light intensity. Electronic delay alignment remains necessary; intensity changes from atmospheric scintillation, collection losses, and instrumental noise still require controls.
Let join the collectors and let be the unit line of sight toward the star. The relevant interferometric baseline is its projection onto the plane of the sky:
The reference arrival-time difference has magnitude , with speed of light . Correct that delay, with a sign fixed by channel order, before averaging the residual correlation at . The physical collector separation equals only when it is perpendicular to ; tracking a star can change the projection even for fixed collectors.
Figure 1.
Functional geometry of stellar intensity interferometry: separate optical detection followed by electrical correlation
. Original schematic with the reference direction normal to the baseline. Matched optical selection feeds independent detectors; mean removal, response and delay alignment precede multiplication and averaging. This is not a scale drawing of the historical apparatus. Details.