# US 2014/0207409 A1 · Method and apparatus for position determination

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- Number: US 2014/0207409 A1
- Document ID: US20140207409A1
- Status: Published application
- Kind: A1
- Application number: 14/232,524
- Filed: 2012-07-13
- Published: 2014-07-24
- Earliest claimed: 2011-07-14
- Assignees: Phase Focus Limited
- Inventors: Fucai Zhang
- Web page: https://patentgrep.com/patent/US20140207409A1

## CPC

- G01B 11/14: for measuring distance or clearance between spaced objects or spaced apertures (G01B11/26 takes precedence; rangefinders G01C3/00)
- G01N 23/046: using tomography, e.g. computed tomography [CT]
- G01N 2223/419: computed tomograph
- G01B: MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)

## Abstract

Embodiments of the invention provide a method of determining a position of an object with respect to incident radiation, comprising iteratively determining at least one of an object function indicating one or more characteristics of an object and a probe function indicative of one or more characteristics of incident radiation, iteratively determining the position of the object, wherein the iteratively determining the position of the object comprises cross correlating first and second estimates of the object function or the probe function, determining a location of a peak of the cross correlation, and determining a translation deviation indicative of a difference in position of the object between the first and second estimates based on the location of the peak.

## Claims

### Claim 1

A method of determining a position of an object with respect to incident radiation, comprising:
iteratively determining at least one of an object function indicating one or more characteristics of an object and a probe function indicative of one or more characteristics of incident radiation;
iteratively determining the position of the object, wherein the iteratively determining the position of the object comprises;
cross correlating first and second estimates of the object, function or the probe function;
determining a location of a peak of the cross correlation;
determining a translation deviation indicative of a difference in position of the object between the first and second estimates based on the location of the peak.

### Claim 2 (depends on 1)

The method of claim 1, wherein the position of the object with respect to the incident radiation is determined at least in part on the translation deviation.

### Claim 3 (depends on 2)

The method of claim 2, wherein the position of the object with respect to the incident radiation is based on the translation deviation and a feedback value.

### Claim 4 (depends on 1)

The method of claim 1, wherein the position of the object is determined based upon the translation deviation and a currently estimated position of the object.

### Claim 5 (depends on 1)

The method of claim 1, wherein the determining the location of the peak of the cross correlation comprises:
determining an integer location of the peak and a sub-integer location of the peak.

### Claim 6 (depends on 1)

The method of claim 1, wherein the cross correlation of the first and second estimates of the object function or the probe function are determined in a frequency domain.

### Claim 7 (depends on 1)

The method of claim 1, wherein the first estimate is a prior estimate of the object function or the probe function and the second estimate is an updated estimate of the object function or the probe function, the method further comprising:
transposing and conjugating the first estimate and determining a transform thereof and determining a transform of the second estimate.

### Claim 8 (depends on 7)

The method of claim 7, further comprising:
multiplying the transforms of the transposed and conjugated first estimate and the second estimate.

### Claim 9 (depends on 8)

The method of claim 8, further comprising:
inversely transforming the multiplied transforms of the transposed and conjugated first estimate and the second estimate.

### Claim 10 (depends on 9)

The method of claim 9, wherein the location of the peak of the cross correlation is determined based on the inversely transformed first estimate and the second estimate.

### Claim 11 (depends on 5)

The method of claim 5, further comprising:
transposing and conjugating the first estimate and determining a transform thereof and determining a transform of the second estimate;
multiplying & and conjugated first estimate and the second estimate; and
zero padding the multiplied transforms to determine the sub-integer location of the peak.

### Claim 12 (depends on 5)

The method of claim 5, further comprising:
transposing and conjugating the first estimate and determining a transform thereof and determining a transform of the second estimate;
multiplying the transforms of the transposed and conjugated first estimate and the second estimate; and
determining an approximate location of the peak and only multiplying a region of the transforms corresponding to the approximate location of the peak to determine the sub-integer location of the peak.

### Claim 13 (depends on 1)

The method of claim 1, wherein the position of the object with respect to the incident radiation is determined for a plurality of positions.

### Claim 14 (depends on 13)

The method of claim 13, wherein the plurality of positions are positions of the object with respect to the incident radiation.

### Claim 15 (depends on 14)

The method of claim 14, wherein in a first iteration of the method an initial estimate of one or both the object function and/or the probe function is utilised.

### Claim 16 (depends on 1)

The method of claim 1, further comprising:
updating only one of the object function and the probe function for a first plurality of iterations.

### Claim 17 (depends on 16)

The method of claim 16, wherein the position of the object with respect to the incident radiation is determined following a second plurality of iterations.

### Claim 18 (depends on 1)

The method of claim 1, wherein the position of the object with respect to the incident radiation is determined iteratively alongside an estimate of one or both the object function or the probe function for at least some iterations.

### Claim 19 (depends on 3)

The method of claim 3, wherein the feedback value is dynamically adjusted.

### Claim 20 (depends on 19)

The method of claim 19, wherein the dynamic adjustment is based on the translation deviation.

### Claim 21 (depends on 19)

The method of claim 19, wherein the dynamic adjustment is provided to reduce the feedback value to avoid instability.

### Claim 22

An apparatus for determining a position of an object with respect to incident radiation, comprising:
a detector for measuring an intensity of a wavefield incident thereon scattered from an object; and
a processing device arranged:
to receive intensity data from the detector,
to iteratively determine at least one of an object function indicating one or more characteristics of the object and a probe function indicative of one or more characteristics of incident radiation, and
to iteratively determine the position of the object with respect to the incident radiation by:
cross correlating first and second estimates of the object function or the probe function indicating of one or more characteristics of the incident radiation,
determining a location of a peak of the cross correlation and
determining a translation deviation indicative of a difference in position of the object between the first and second estimates based on the location of the peak.

### Claim 23 (depends on 22)

The apparatus of claim 22, wherein the position of the object with respect to the incident radiation is based on the translation deviation and a current estimate of the location of the object.

### Claim 24 (depends on 22)

The apparatus of claim 22, wherein the processing device is further arranged to:
determine the position of the object with respect to the incident radiation based on the translation deviation and a feedback value.

### Claim 25 (depends on 22)

The apparatus of claim 22, wherein the processing device is further arranged to:
determine the location of the peak of the cross correlation by determining an integer location of the peak and a sub-integer location of the peak.

### Claim 26 (depends on 22)

The apparatus of claim 22, wherein the processing device is further arranged to:
determine the cross correlation of the first and second estimates of the object function or the probe function in a frequency domain.

### Claim 27 (depends on 22)

The apparatus of claim 22, wherein the first estimate is a prior estimate of the object function or the probe function and the second estimate is an updated estimate of the object function or the probe function, wherein the processing device is further arranged to:
transpose and conjugate the first estimate and to determine a transform thereof and determine a transform of the second estimate.

### Claim 28 (depends on 27)

The apparatus of claim 27, wherein the processing device is further arranged to:
multiply the transforms of the transposed and conjugated first estimate and the second estimate.

### Claim 29 (depends on 28)

The apparatus of claim 28, wherein the processing device is further arranged to:
inversely transform the multiplied transforms of the transposed and conjugated first estimate and the second estimate.

### Claim 30 (depends on 29)

The apparatus of claim 29, wherein the processing device is further arranged to:
determine the location of the peak of the cross correlation based on the inversely transforming the multiplied transforms of the transposed and conjugated first estimate and the second estimate.

### Claim 31 (depends on 25)

The apparatus of claim 25, wherein the processing device is further arranged to:
transpose and conjugate the first estimate and to determine a transform thereof and determine a transform of the second estimate;
multiply the transforms of the transposed and conjugated first estimate and the second estimate; and
zero pad the multiplied transforms to determine the sub-integer location of the peak.

### Claim 32 (depends on 25)

The apparatus of claim 25, wherein the processing device is further arranged to:
transpose and conjugate the first estimate and to determine a transform thereof and determine a transform of the second estimate;
multiply the transforms of the transposed and conjugated first estimate and the second estimate; and
determine an approximate location of the peak and to only multiply a region of the transforms corresponding to the approximate location to determine the sub-integer location of the peak.

### Claim 33

(canceled)

### Claim 34

A non-transitory computer-readable medium containing computer executable instructions which, when executed by a computer, perform operations comprising:
iteratively determining at least one of an object function indicating one or more characteristics of an object and a probe function indicative of one or more characteristics of incident radiation; and
iteratively determining the position of the object, wherein the iteratively determining the position of the object comprises:
cross correlating first and second estimates of the object function or the probe function;
determining a location of a peak of the cross correlation; and
determining a translation deviation indicative of a difference in position of the object between die first and second estimates based on the location of the peak.