Sampling in 2D

1 Junho 2026, 14:00 • José Manuel Rebordão

Examples of correct and incorrect sampling.
2D sampling modelling, including pixel area.
Artifacts in 2D. Anti-aliasing techniques.
Superposition of periodic patterns. Analysis in the frequency plane. Visual MTF and Contrast Sensitivity Function. Visibility circle.
Frequency linear combinations leading to the Visibility Circle.
Stable and unstable states. Applications of unstable superpositions. Examples. Hidden information. Document security.
 
END OF THE COURSE

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Optical Detection Architectures

29 Maio 2026, 09:00 • José Manuel Rebordão

Superposition of periodic patterns. Moiré patterns. Similarity with the mathematics of interference.
Modulation and demodulation.
Heterodyne and homodyne detection architectures. Balanced homodyne.
Examples of heterodyne and homodyne phase and/or amplitude modulation and demodulation.
 
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Sampling in 2D

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Wavefront metrology (class 3 of 3)

27 Maio 2026, 15:00 • Alexandre Pereira Cabral

A Shack-Hartmann wavefront sensor was built based on an array of lenses that divide / sample the incoming wavefront into small sub-apertures, focusing independently the light from each lens in a 2D sensor that captures the focal plane pattern. This pattern was processed to obtain the position of each focus point from each individual lens.

An incident plane wave was created using a spatial filter and a collimated lens to produce a grid of equidistant focal points, the reference position, while several distorted waves (corresponding to a point source from an optical fibre in controlled positions) result in an uneven distribution of points that were referenced to the ideal plan wave situation in order to determine with the sensor the position of the fibre tip, using the Shack-Hartman sensor to measure an unknown wavefront based of the focus shifts from the calibration.

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SRC. PDH stabilization

25 Maio 2026, 14:00 • José Manuel Rebordão

SRC – Simplified model relating the SRC with the transfer function
Pound-Drever-Hall stabilization technique: principles, error function
 
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Optical Detection architectures

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Recycling cavities

22 Maio 2026, 09:00 • José Manuel Rebordão

Dual resonant MI. Carrier at the SYM port, +1 reflectivity. GW signal at the ASY port.
Power recycling concept.
Single arm, three mirrors and two coupled cavities, maximization of the arms intracavity power. Field at the SYM port.
Power recycled MI, Small MI (SMI) defined with the BS. Coupling three cavities, PRC, SMI and Arms. Output at the ASY port. Resonances and anti-resonances.
Cavities’ poles analysis. Example of aLIGO.
Signal recycling concept and overview of tuning.
 
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SRC. 

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