Fourier domain sensing

A method for measuring one or more sinusoidal spatial Fourier-transform components of an object, the method comprising:

• illuminating the object with a first probing radiation comprising one or more plane-wave components having distinct directions of propagation, wherein the object produces a second radiation in response to such illuminating;
• imparting a distinct frequency shift on each of the probing radiation components;
• detecting, with a single-element detector, a third reference radiation substantially coherent with respect to the first probing radiation and a portion of the second radiation from a plurality of locations on the object substantially simultaneously;
• and
• estimating at least one characteristic of the one or more sinusoidal spatial Fourier-transform components of the object based on a time-varying signal from the detected second and third radiations.

A method for measuring one or more plane-wave components of a first radiation, the method comprising:

• illuminating a single-element detector with the first radiation and with a second radiation substantially coherent with respect to the first radiation, the second radiation comprising one or more plane-wave components having distinct directions of propagation;
• imparting a distinct frequency shift on each of the second radiation components;
• detecting the first and second radiations with the detector substantially simultaneously;
• and
• estimating at least one of amplitude, phase, or direction of propagation of the one or more plane-wave components of the first radiation based on a time-varying signal due to the detected radiations.

A method for measuring one or more sinusoidal spatial Fourier-transform components of a portion of an image formed by a first radiation, the method comprising:

• generating a structured third radiation by spatially modulating a second radiation;
• illuminating a single-element multiphoton detector with the structured third radiation and with the first-radiation image portion;
• detecting the first and third radiations with the multiphoton detector substantially simultaneously;
• and
• estimating a characteristic of the one or more sinusoidal spatial Fourier-transform components of the portion of the image based on a time-varying signal due to the detected radiations.

A method for measuring a sinusoidal spatial Fourier-transform component of a portion of an image formed by a first radiation, the method comprising:

• spatially modulating an amplitude of the portion of the image with a traveling modulation pattern to form a structured second radiation;
• detecting a portion of the structured second radiation from a plurality of locations on the image substantially simultaneously;
• and
• estimating a characteristic of the sinusoidal spatial Fourier transform component of the portion of the image based on a time-varying signal due to the detected radiation.