Abstract: Disclosed are method and electronic components for: i) electronically extracting a sequence of values from a measurement signal corresponding to a position of a moving object, wherein the sequence of values indicates the position of the moving object at corresponding time increments; ii) electronically determining at least one of an estimate for a velocity of the moving object and an estimate for an acceleration of the moving the object based on a plurality of the values in the sequence of values; and iii) electronically correcting a value in the sequence of values to substantially reduce the effect of processing and signal delays based on one or both of the velocity and acceleration estimates.

Abstract: A method includes obtaining, from a detector of an interferometry system, an interference signal based on a combination of a first beam and a reference beam, subsequent to the first beam being diffracted by an encoder scale, obtaining, through an electronic processor, an error compensation signal based on a non-harmonic cyclic error that modifies the interference signal, and outputting information about a change in a position of the encoder scale relative to an optical assembly of the interferometry system based on the interference signal and the error compensation signal.

Abstract: Methods and apparatuses for performing the same, where the methods include obtaining, from an interferometer, a time-varying interference signal S(t) based on a combination of a first beam and a second beam, the first beam being diffracted from an encoder scale, in which at least one of the encoder scale and the interferometer is moveable with respect to the other, obtaining one or more error correction signals based on one or more errors that modify the time-varying interference signal S(t), and outputting information about a change in a position of the encoder scale relative to the interferometer based on the time-varying interference signal S(t) and the one or more error correction signals.

Abstract: A method includes obtaining, from a detector of an interferometry system, an interference signal based on a combination of a first beam and a reference beam, subsequent to the first beam being diffracted by an encoder scale, obtaining, through an electronic processor, an error compensation signal based on a non-harmonic cyclic error that modifies the interference signal, and outputting information about a change in a position of the encoder scale relative to an optical assembly of the interferometry system based on the interference signal and the error compensation signal.

Abstract: Methods and apparatuses for performing the same, where the methods include obtaining, from an interferometer, a time-varying interference signal S(t) based on a combination of a first beam and a second beam, the first beam being diffracted from an encoder scale, in which at least one of the encoder scale and the interferometer is moveable with respect to the other, obtaining one or more error correction signals based on one or more errors that modify the time-varying interference signal S(t), and outputting information about a change in a position of the encoder scale relative to the interferometer based on the time-varying interference signal S(t) and the one or more error correction signals.

Abstract: An interference signal S(t) is provided from interference between two beams directed along different paths. The signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths, where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, and t is time. An error signal is provided to reduce errors in an estimate of {tilde over (L)}(t). The error signal is derived at least in part based on one or more collective properties of a distribution of multi-dimensional values. At least one of the multi-dimensional values in the distribution is generated from a plurality of samples of the signal S(t) (e.g., samples of the signal captured at different times).

Abstract: A first portion of a beam including a first frequency component is directed along a first path. A second portion of the beam is frequency shifted to generate a shifted beam that includes a second frequency component different from the first frequency component and one or more spurious frequency components different from the first frequency component. At least a portion of the shifted beam is directed along a second path different from the first path. An interference signal S(t) from interference between the beam portions directed along the different paths is measured. The signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the paths, where n is an average refractive index along the paths, {tilde over (L)}(t) is a total physical path difference between the paths, and t is time.

Abstract: A method is disclosed including conditioning a measurement signal from an interferometer, said conditioning characterized by one or more conditioning parameters; measuring a plurality of values for the conditioned measurement signal; providing one or more values indicative of the conditioning parameters; determining an adjustment value at each measured value of the conditioned measurement signal based on the one or more of the measured values indicative of the conditioning parameters; and adjusting a measured value of the measurement signal according to the adjustment value.

Abstract: A first portion of a beam including a first frequency component is directed along a first path. A second portion of the beam is frequency shifted to generate a shifted beam that includes a second frequency component different from the first frequency component and one or more spurious frequency components different from the first frequency component. At least a portion of the shifted beam is directed along a second path different from the first path. An interference signal S(t) from interference between the beam portions directed along the different paths is measured. The signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the paths, where n is an average refractive index along the paths, {tilde over (L)}(t) is a total physical path difference between the paths, and t is time.

Abstract: The invention features a method including: (i) providing an interference signal S(t) from two beams directed along different paths, wherein the signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths, where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, and t is time; (ii) providing one or more coefficients representative of one or more errors that cause the signal S(t) to deviate from an ideal expression of the form A1 cos(?Rt+?(t)+?1), where A1 and ?1 are constants, ?R is an angular frequency difference between the two beams before being directed along the different paths, and ?(t)=nk{tilde over (L)}(t), with k=2?/? and ? equal to a wavelength for the beams; (iii) calculating a linear combination of values of the signal S(t); and (iv) reducing the effect of the deviation of S(t) from the ideal expression on an estimate of {tilde over (L)}(t) using an e

Abstract: A method and apparatus used to reduce glitches in measurements made by an accumulation of phase changes over a range greater than 2?. Embodiments of the invention feature the use of a glitch filter that receives a phase input indicating a position value. The glitch filter reduces glitches by using a feedback term that has been reduced modulo 2?. The method includes measuring a plurality of values of a measurement signal, determining a current position value based on each of the plurality of measured values, wherein determining includes determining a delta value based on a current measured value and a previous position value, wherein the delta value is reduced modulo 2? to a range of ±?, and determining the current position value based on the determined delta value, and outputting at least one of the determined current position value and a velocity value.

Abstract: A method for compensating data age in measurement signals from an interferometer includes measuring a value of the measurement signal and adjusting the measured value based on the measurement signal with a data age adjustment value to correct for data age.

Abstract: Apparatus and methods particularly suitable for use in electro-optical metrology and other applications to measure and monitor the refractive index of a gas in a measurement path and/or the change in optical path length of the measurement path due to the gas while the refractive index of the gas may be fluctuating due to turbulence or the like and/or the physical length of the measuring path may be changing. More specifically, the invention employs electronic frequency processing to provide measurements of dispersion of the refractive index, the dispersion being substantially proportional to the density of the gas, and/or measurements of dispersion of the optical path length, the dispersion of the optical path length being related to the dispersion of the refractive index and the physical length of the measurement path.

Abstract: Apparatus and methods particularly suitable for use in electro-optical metrology and other applications to measure and monitor the refractive index of a gas in a measurement path and/or the change in optical path length of the measurement path due to the gas while the refractive index of the gas may be fluctuating due to turbulence or the like and/or the physical length of the measuring path may be changing.

Abstract: Apparatus and methods particularly suitable for use in electro-optical metrology and other applications to measure and monitor the refractive index of a gas in a measurement path and/or the change in optical path length of the measurement path due to the gas while the refractive index of the gas may be fluctuating due to turbulence or the like and/or the physical length of the measuring path may be changing. Apparatus and method for measuring effects of the refractive index of a gas in a measurement path wherein the phase redundancy is resolved for phase signals.

Abstract: A method and apparatus used to reduce glitches in measurements made by an accumulation of phase changes over a range greater than 2&pgr;. Embodiments of the invention feature the use of a glitch filter that receives a phase input indicating a position value. The glitch filter reduces glitches by using a feedback term that has been reduced modulo 2&pgr;.

Abstract: Apparatus and methods particularly suitable for use in electro-optical metrology and other applications to measure and monitor the refractive index of a gas in a measurement path and/or the change in optical path length of the measurement path due to the gas while the refractive index of the gas may be fluctuating due to turbulence or the like and/or the physical length of the measuring path may be changing. More specifically, the invention employs electronic frequency processing to provide measurements of dispersion of the refractive index, the dispersion being substantially proportional to the density of the gas, and/or measurements of dispersion of the optical path length, the dispersion of the optical path length being related to the dispersion of the refractive index and the physical length of the measurement path.

Abstract: Apparatus and methods particularly suitable for use in electro-optical metrology and other applications to measure and monitor the refractive index of a gas in a measurement path and/or the change in optical path length of the measurement path due to the gas while the refractive index of the gas may be fluctuating due to turbulence or the like and/or the physical length of the measuring path may be changing. More specifically, the invention employs electronic frequency processing to provide measurements of dispersion of the refractive index, the dispersion being substantially proportional to the density of the gas, and/or measurements of dispersion of the optical path length, the dispersion of the optical path length being related to the dispersion of the refractive index and the physical length of the measurement path.

Abstract: Apparatus and methods particularly suitable for use in electro-optical metrology and other applications to measure and monitor the refractive index of a gas in a measurement path and/or the change in optical path length of the measurement path due to the gas while the refractive index of the gas may be fluctuating due to turbulence or the like and/or the physical length of the measuring path may be changing. More specifically, the invention employs electronic frequency processing to provide measurements of dispersion of the refractive index, the dispersion being substantially proportional to the density of the gas, and/or measurements of dispersion of the optical path length, the dispersion of the optical path length being related to the dispersion of the refractive index and the physical length of the measurement path.

Abstract: Apparatus and methods particularly suitable for use in electro-optical metrology and other applications to measure and monitor the refractive index of a gas in a measurement path and/or the change in optical path length of the measurement path due to the gas while the refractive index of the gas may be fluctuating due to turbulence or the like and/or the physical length of the measuring path may be changing. More specifically, the invention employs electronic frequency processing to provide measurements of dispersion of the refractive index, the dispersion being substantially proportional to the density of the gas, and/or measurements of dispersion of the optical path length, the dispersion of the optical path length being related to the dispersion of the refractive index and the physical length of the measurement path.