WO2009081121A1

WO2009081121A1 - Distance measurement

Info

Publication number: WO2009081121A1
Application number: PCT/GB2008/004198
Authority: WO
Inventors: David Burton
Original assignee: Liverpool John Moores University
Priority date: 2007-12-21
Filing date: 2008-12-18
Publication date: 2009-07-02
Also published as: GB0724948D0

Abstract

A method of determining a distance, a method of measuring a distance and associated apparatus are described. A method of determining a distance relative to an object includes determining the phase difference between a first beam of radiation of a first wavelength incident on an object along a predetermined path, and a second beam of radiation of a second, different wavelength incident on the object along the predetermined path. The distance relative to the object along the path can be calculated utilising the determined phase difference, the wavelength difference between the two wavelengths, the value of one of said wavelengths, and an approximate distance relative to the object. The topography of an object can be calculated, by measuring a number of distances relative to different positions on an object.

Description

DISTANCE MEASUREMENT

The present invention relates to methods of determining distances to objects, and includes methods of measuring distances to objects, and associated apparatus. A variety of devices and methods exist for measuring distances.

Approximate distances can be measured using a variety of apparatus, including mechanical devices such as rulers or tape measures. Optical devices such as laser range finders are generally available, which allow distance measurements to be performed to within an accuracy of millimetres or less. Such devices direct a laser pulse at an object, and determine the distance to the object based upon the time taken for the reflected pulse to return.

Taking a number of distance measurements can allow topographic profiles of objects, or locations including such objects, to be determined e.g. surveyors typically take a number of distance measurements from a number of different locations when performing surveys.

Interferometers can be utilised to perform more accurate distance measurements e.g. to measure distances to an accuracy of the order of microns. Most interferometers are only capable of measuring relative distances. Interferometers are instruments in which two or more radiation beams (including acoustic, optical or microwave) are arranged to form an interference pattern of fringes. Interferometers can be used in a number of distance measurements applications. The article by Jack A. Stone et al, "Diode Lasers in Length Metrology: Application to Absolute Distance Interferometry", CaI Lab, The International Journal of Metrology, November- December 1999, pages 1-7, describes a distance measurement method using a wavelength-sweeping technique for absolute interferometry. The technique utilises a tunable laser source of approximate wavelength 670nm, which is tuned across a wavelength range of about 8nm.

The interferometer consists of two arms, one arm of unknown length, and one reference arm of fixed, known length. A laser beam is directed along both arms, with the reflected beams interfering at the interferometer output. The technique measures the change in an interference fringe pattern as the wavelength is swept across the range of 8nm. The position of the fringes will move during the wavelength sweep, and the technique effectively counts the number of fringes passing a given point. The number of fringes is proportional to the product of the laser frequency shift, and to the difference between the unknown length arm of the interferometer and the fixed length arm of the interferometer. Hence, by knowing the change in wavelength frequency and the length of the fixed arm of the interferometer, the length of the unknown arm (e.g. the distance to an object) can be calculated. In order to provide an accurate measurement, it is desirable to count the maximum possible number of fringes i.e. to sweep the laser across as great as possible a wavelength range.

A major disadvantage associated with prior art interferometry measurement techniques is the cost of the measurement apparatus. The laser source must be able to sweep over a relatively large wavelength range, whilst maintaining a stable output. Further, to measure large distances, it is generally desirable that the coherence length of the laser beam is relatively large e.g. the coherence length must be at least twice the difference between the maximum length to be measured and the known fixed length arm of the interferometer. Providing such a laser source, can be expensive. Many lasers are unsuitable for sweeping over relatively wide wavelength ranges. Although such sources can include relatively cheap laser diodes, providing the necessary tunable external cavity to allow the wavelength to sweep over a laser wavelength range can be expensive. Further, so as to enable the number of fringes to be counted, many implementations require a continuous line of sight of the fringe pattern, as well as for the laser to be absolutely stable as the wavelength sweep occurs. Any interruption of the laser beam (or any loss of the line of sight to the fringes) as the wavelength is being swept across the wavelength range, can prevent the number of fringes being accurately counted, and hence lead to errors e.g. any mode hops will disrupt the measurement. In order to suitably stabilise the laser over the sweep range, Zeeman stabilisation may be required.

It is an aim of embodiments of the present invention to address one or more problems of the prior art, whether referred to herein or otherwise. It is an aim of a particular embodiment of the present invention to allow a relatively accurate distance measurement to be performed, once an approximate distance measurement has been made. According to an aspect of the present invention, there is provided a method of determining a distance relative to an object, the method comprising: determining the phase difference between a first beam of radiation of a first wavelength incident on an object along a predetermined path, and a second beam of radiation of a second, different wavelength incident on the object along the predetermined path; determining the difference between the first and second wavelengths; calculating the distance relative to the object utilising the determined phase difference, the determined wavelength difference, the value of one of said wavelengths, and an approximate distance relative to the object. The present inventor has realised that an accurate distance measurement can be made using knowledge of an approximate distance relative to an object, and the other above information. Such a technique can be relatively cheaply and easily implemented. Unlike prior art techniques which involve continuous sweeping of the source over a predetermined range of wavelength, this technique can be performed at two discrete wavelengths i.e. the technique does not require complex and expensive laser sources arranged to stably sweep the output wavelength over a continuous wavelength range. As the technique only needs to take into account the relative difference between the phases of the two radiation beams, a continuous line of sight is also not required whilst the change in radiation beam wavelength is performed. Preferably, the approximate distance relative to the object is known to within an accuracy of ± AD , where

_{± AD <}A^_, 2δλ where δλ is the difference between the two wavelengths, λj is the first wavelength and λ₂ is the second wavelength. Preferably, the phase difference is determined at a plurality of different positions across the width of said path, and the distance relative to the object is calculated for each of said positions.

Preferably, the phase difference between the radiation beams is determined by: analysing a first interference pattern formed from a portion of the first beam of radiation reflected from the object; analysing a second interference pattern formed from a portion of the second beam of radiation reflected from the object; and comparing the analysis of the first interference pattern with the second interference pattern. Preferably, the interference patterns are analysed using Fourier transform fringe analysis.

Preferably, the method further comprises calculating the maximum and minimum values for the difference Δn between the number of waves of the first radiation beam along the predetermined path, and the number of waves of the second beam of radiation along the predetermined path, based upon the wavelengths of the radiation beams and the maximum and minimum possible values of the approximate distance. Preferably, the method further comprises calculating the value of a parameter

D indicative of the distance relative to the object,

_ A₁(A₁ + #l)

D = δλ 2π where λi is the wavelength of the first radiation beam, δλ is the difference in wavelength between the two radiation beams, δ φ is the determined phase difference, ΔN is an integer difference in the number of waves of the first radiation beam along the predetermined path and of the second radiation beam along the predetermined path.

Preferably, the values of D are calculated for the values of ΔN determined using the calculating of the maximum and minimum values for the difference ΔN between the number of waves of the first radiation beam along the predetermined path, and the number of waves of the second beam of radiation along the predetermined path, based upon the wavelengths of the radiation beams and the maximum and minimum possible values of the approximate distance, so that the value of D falling between the maximum and minimum possible values of the approximate distance is determined as the actual distance.

According to a second aspect of the present invention, there is provided a method of measuring a distance relative to an object, comprising: providing a first beam of radiation incident on the object along a predetermined path; and providing a second beam of radiation of a second, different wavelength incident on the object along the same path; and performing the method according to the first aspect of the present invention. Preferably, the method further comprises measuring the approximate distance relative to the object.

Preferably, the object is at least partially reflective.

Preferably, the object is a mirror placed a predetermined distance from a further object, the method further comprising determining the distance to the further object based upon the predetermined distance and the calculated distance relative to the object.

Preferably, the approximate distance relative to the object is measured within an error of ±ΔD, and the maximum difference in wavelength between the second

wavelength and the first wavelength λj is calculated by SA_n^₁₁ = — - — .

2ΔD

Preferably, the method further comprises selecting the wavelength of the second radiation beam such that the different δλ between the first wavelength and the second wavelength satisfies the relationship δλ_maχ/2 < δλ < δλ_max.

Preferably, said beams are incident on the object on a surface of the object extending transverse, but not perpendicular to, the predetermined path.

Preferably, the method further comprises forming an interference pattern between a reflected portion of the first radiation beam and a respective reference beam; forming an interference pattern between a reflected portion of the second radiation beam and a respective reference beam; and determining the phase difference from said interference patterns.

Preferably, said reference beams are both directed along a predetermined reference path and reflected from a surface of a reference mirror.

Preferably, the reference mirror extends transverse, but not perpendicular to, the path of the incident reference beams. Preferably, at least one of the surfaces is planar.

Preferably, the first radiation beam and the respective reference beam are formed from a first main beam split by a beam splitter, and the second radiation beam and the respective reference beam are formed from a second main beam split by a beam splitter, the relative distance being the total distance along the beam path from the surface of the reference mirror to the beam splitter, and from the beam splitter to the object. Preferably, said interference patterns are formed on the input of an image capture device arranged to capture an electronic image of each interference pattern for analysis thereof.

According to a third aspect of the present invention there is provided a method of forming a topographic profile of an object, comprising: performing the method according to the first or second aspect of the present invention, for a variety of different predetermined paths to different positions on the object; and calculating a topographic profile for the object based upon the relative distance calculated for each path. According to a forth aspect of the present invention, there is provided a method of forming a topographic profile of an object, comprising: performing the method according to the first aspect of the present invention, wherein the phase difference is determined at a plurality of different positions across the width of said path, and the distance relative to the object is calculated for each of said positions; and calculating a topographic profile for the object based upon the relative distances calculated for each of said positions.

According to a fifth aspect of the present invention, there is provided a carrier medium carrying computer readable program code configured to cause a computing device to carry out a method according to any of the first to forth aspects of the present invention.

According to a fifth aspect of the present invention, there is provided a device for controlling an interferometer to carry out a distance measurement, the device comprising: a program memory containing processor readable instructions; and a processor configured to read and execute instructions stored in said program memory; wherein said process readable instructions comprise instructions configured to control said device to carry out a method according to any of the first to forth aspects of the present invention.

According to a sixth aspect of the present invention, there is provided a device for determining a distance relative to an object, the device comprising: a radiation source for providing a first beam of radiation of a first wavelength, and a second beam of radiation of a second, different wavelength incident on the object along the same path; a measurement device to determine the phase difference between the first beam of radiation incident on the object and the second beam of radiation incident on the object.; a computational device arranged to carry out the method according to any of the first to forth aspects of the present invention.

Preferably, the difference in wavelength between the two beams is less than 5nm.

Preferably, the device comprises an interferometer.

According to any aspect of the invention, a distance relative to a moving object may be determined. A dynamic measurement of the distance relative to the moving object may be determined by repeating the method. Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

Figure 1 is a schematic diagram of a device for measuring distance in accordance with an embodiment of the present invention;

Figure 2 is a schematic diagram indicating plane waves of a radiation beam of a first wavelength travelling from a radiation source to a target object;

Figure 3 is a schematic diagram indicating plane waves of a radiation beam of a second wavelength travelling the same distance as in Figure 2 from a radiation source to a target object;

Figure 4 indicates the intensity function of a first interference pattern corresponding to a first radiation beam of a first wavelength reflected from an object;

Figure 5 indicates the intensity function of a second interference pattern corresponding to a second radiation beam of a first wavelength reflected from the object;

Figure 6 is a schematic diagram of a device for measuring distance in accordance with a further embodiment of the present invention; and

Figure 7 is a schematic diagram of a device for measuring distance in accordance with another embodiment of the present invention.

Figure 1 shows a device 100 suitable for measuring a distance to an object. The device comprises a radiation source 10, arranged to supply a first radiation beam having a first wavelength λi, and a second radiation beam having a second, different wavelength λ₂. The device comprises two reflective surfaces 12, 14. Typically, each reflective surface will be a mirror. Preferably, each reflective surface 12, 14 is a planar surface. Preferably, each reflective surface is a planar surface over at least the portion of the surface from which the relevant radiation beams reflect.

The radiation source can be any source of electromagnetic or acoustic radiation, but is more preferably optical radiation. The radiation source 10 is arranged to direct each radiation beam along a path 30 towards the first reflective surface 12. A beam splitter 16 is arranged in the beam path between the radiation source 10 and the reflective surface 12. Beam splitter 16 could for instance take the form of a half- silvered beam splitting mirror, with reflective surfaces 12 and 14 being implemented as plane mirrors. The beam splitter is arranged to transmit a predetermined portion of incident radiation along a path 36 towards the first reflective surface 12, and to direct (e.g. reflect) a portion of the incident radiation along a path 32 towards the second reflective surface 14.

Radiation directed from the beam splitter 16 along path 32 towards second reflective surface 14 is reflected by that surface, back generally along path 32, towards the beam splitter 16. The reflected light from path 32 incident on the beam splitter 16 is then transmitted through the beam splitter 16 (or at least a portion of that radiation is transmitted through the beam splitter 16) on a path 34 towards an imaging screen 18. The first reflective surface 12 is arranged to reflect incident light from the beam splitter 16 back towards the beam splitter 16 substantially back along incident path 36. The beam splitter 16 is arranged to direct (reflect) that light from the reflective surface 12 along a path 38 towards the imaging screen 18.

Thus, radiation reflected from the first surface and radiation reflected from the second surface will be incident on the image screen 18, and will form an interference pattern on that screen. It should be appreciated that, whilst the interference pattern is displayed on image screen 18, technically the point of interference of the two reflected beams is at the recombinant of the beam splitter 16. Thus, the interference fringes will exist anywhere along the path 34, 38, and will be displayed on a screen inserted anywhere along that path.

At least one of the reflective surfaces 12, 14 is not perpendicular to the path of the respective incident beam 36, 32. hi the particular embodiment shown in Figure 1, one of the surfaces (mirror 14) extends perpendicular to the path of the respective incident radiation beam (32), and the other reflective surface (12) extends at an angle θ with respect to the plane perpendicular to the incident radiation beam path 36.

Typically, θ will be a relatively small angle i.e. of the order of 0.01 to 0.03 degrees e.g. θ could be less than 0.1 or 0.05 degrees, θ may be chosen so as to ensure a difference in path length across the incident beam of between 10 and 100 times the wavelength of the electromagnetic radiation constituting the incident beam. For example, in practice this may imply a value of θ in the range of 0.01 to 0.5 degrees.

Consequently, the interference pattern 180 formed by the reflective beams 34, 38 will appear as a series of fringes 181. The fringes contour the tilt of the angled reflective surface 12, and indicate a contouring interval of λ/2, where λ is the wavelength of the radiation beam. Assuming the angled reflective surface is a planar surface, then the fringes will be straight and have a regular spacing d, with d being a function of θ. It will be appreciated that the apparatus 10, 12, 14, 16, 18 is generally in the form of an interferometer e.g. a Michelson interferometer. hi this particular embodiment, the interferometer output (i.e. the interference pattern formed by the reflected beams) is digitally captured. In particular, imaging screen 18 is the input of an image capture device e.g. a CCD (charge coupled device). The captured image is then provided to a computational device 20 (e.g. a computer or microprocessor), which is arranged to perform calculations to calculate a desired distance, as described herein. In preferred embodiments, the device 20 is also arranged to control the operation of the interferometer apparatus.

The interferometer can be regarded as having two arms, each arm corresponding to a respective beam path from the radiation source to the interferometer output (i.e. imaging screen 18). Thus, a first arm can be regarded as including radiation beams paths 30, 36 to first reflective surface 12, and back from the first reflective surface along radiation path 36 to the beam splitter, and then along path 38 to the interferometer output 18. The second arm can be regarded as being along radiation path 30 to beam splitter 16, then from beam splitter 16 along path 32 to the second reflective surface 14, and then from the second reflective surface 14 back via path 32 through the beam splitter 16 along path 38 (which is generally the same as path 34) to the interferometer output.

Within the interferometer, one arm generally acts as a reference arm, to provide a reference beam to form the interference fringe at the interferometer output with the beam from the other arm. The other arm acts as the arm along which the relevant distance measurement is performed. Either arm can act as the reference arm i.e. either of reflective surfaces 12, 14 could act as a reference mirror. However, for the sake of convenience, in this particular example, the second arm will be described as acting as the reference arm to provide the reference beam i.e. second reflective surface 14 is the reference mirror.

The first arm, including reflective surface 12, therefore acts as the measurement arm. The distance measurement as described herein will measure the distance D = D_ref + D_meas, where D_ref is the distance from the beam splitter 16 to the reference reflective surface (i.e. mirror 14), and D_meas is the distance from the beam splitter 16 to reflective surface 12. In most instances, the distance along the reference arm (i.e. from beam splitter 16 to reflective surface 14) will be a constant, and hence the technique can be utilised to determine the distance from the beam splitter 16 to reflective surface 12.

The reflective surface 12 could be a surface of an object, in which case the distance measurement will determine the distance from the radiation source 10 to the object.

Alternatively, reflective surface 12 could be a reflective surface that is located in a predetermined relationship (distance and orientation) relative to the object. Measurement of the distance from the source 10 to the reflective surface 12 would, in such an instance, then allow the distance from the source 10 to the object to be calculated, by taking into account the relative orientation and positioning of the reflective surface 12 to that object. For example, reflective surface 12 could, in such an incidence, be a mirror with a probe attached, with the probe being positioned so as to be in contact with the object. A method of utilising the apparatus will now be described.

The source 10 is arranged to provide a first radiation beam of a first wavelength λi along path 30, such that an interference pattern is formed on the imaging screen 18, with the interference fringes contouring the tilt of the reflective surface 12. The fringes in the fringe pattern will thus be a series of nominally straight interference fringes, contouring the tilt of the reflective planar surface 12, and having a contouring interval of λi/2. The interference pattern is captured by the image capture device 18.

The radiation source then provides a second radiation beam of a second, different wavelength λ₂ along radiation path 30, so as to provide a resulting second interference pattern at the interferometer output. The second interference pattern is then captured by image capture device 18. Again, the interference pattern will consist of nominally straight interference fringes, which contour the tilt of the target mirror 12. However, as the wavelength is different, the fringes will have a different spacing as the fringes in the second interference pattern will instead provide a contouring interval of λ₂/2. Typically, as the difference in wavelength between λ_\ and λ₂ will be relatively small (e.g. lnm or less), then the change in fringe spacing is insignificant. However, the change in phase (the phase shift) between the fringes from the two different wavelengths λ_\ and λ₂ will be significant, as the distance being measured is long compared to the wavelengths.

The captured images of the interference pattern are then analysed by device 20. In particular, the relative phases of the fringes are determined. The phases of the fringes can be calculated using FTFA (Fourier Transform Fringe Analysis). A corresponding position is selected on each image, (corresponding to the same position on the image screen) and the phase difference δ φ between the two images calculated at that position. Typically, for convenience the centre point of each image would be chosen as the basis for calculating δ φ , although in practice any two corresponding positions could be selected.

An approximate measurement D_app_rox is then made of the D, the total distance from the reflective surface 14 to the beam splitter 16 and then to the reflective surface 12 along the beam path (i.e. the reflective surface of the object to which the distance measurement is being made). This approximate measurement, D_app_roχ should be made to an accuracy of ± AD, where

2δλ where δλ is the difference between the two wavelengths, λ_\ is the first wavelength, and λ₂ is the second wavelength. Typically, as δλ is small, λ_\ ~ X₁ , and so this λ,² accuracy can be approximated as = ± AD <

2δλ

Such an approximate distance measurement, in conjunction with the determined phase difference δφ between the interference fringes, can allow the distance D to be determined to a great accuracy.

Over the distance D, there will be a first number of complete waves of the first radiation beam. Correspondingly, there will be a second, different number of complete waves of the second wavelength over the distance D. Measuring D to within the error value indicated above, restricts the value ΔN (the integer difference between the first and second numbers of waves) to be one of two integer values. These two integer values can be calculated from the maximum and minimum possible distances of D (i.e. D_max = D_app_rox + ΔD, and D_1nJn = D_approx -ΔD). Based on the two possible values for ΔN, the distance can then be calculated to great accuracy. In particular, the actual distance D can be calculated using the expression

for both possible values of ΔN. Only one value will be within the range D_apProx + ΔD - that value is the accurate measurement of distance D.

As D_ref will typically be a known constant, the unknown distance D_meas can be calculated :

D_meas = D-D_ref.

In order that the skilled person can understand the various permutations of measuring and determining distances that may be performed in accordance with the invention, the basic concepts underlining the invention will now be explained, with reference to Figures 2-5. Further embodiments will then be explained with reference to Figures 6 & 7.

Turning to Figure 2, consider a collimated light source 10 located at a point in space (xyz), and emitting a radiation beam 30 of predetermined wavelength λi. Plane waves emanate from the source 10 towards a target e.g. a surface 12. Assume that it is desirable to determine the example distance D_ex from the radiation source 10 to the surface 12 to a relatively high accuracy (e.g. preferably significantly greater than 1 μm).

A finite, typically very large, number of waves must exist between the source and the target. For convenience, there are only approximately 5.5 waves between the source 10 and the target surface 12 in Figure 2.

The exact number of waves n_t between source and 10 can be calculated by:

A₁

It will be appreciated that, if values of n_\ and λ) were known, then it would be possible to calculate D_ex. However, whilst for most radiation sources (particularly lasers), it is possible to know the wavelength λi to a great accuracy, it is generally relatively difficult to determine the value of ni.

Figure 3 shows the same source and the same distance D_ex from the target 12.

However, the source is changed so as to emit radiation of wavelength λ₂, where X₁ differs from λ_\ by an amount δλ (i.e. δλ is the difference between the two wavelengths λi and λ₂). Consequently the number of waves in the distance D_ex will change (4 waves are indicated in Figure 3 to illustrate this effect). The actual number of waves n₂ in the example distance D_ex can be calculated by:

n₂ = ^ (2)

A₂

Defining a variable Δn, as the change in the number of waves as the wavelength is changed,

Δn = «, - n₂ (3)

The technique described herein utilises the principle that whilst it is difficult to know n_! or n₂ to any degree of accuracy, in certain circumstances it is possible to find a value for Δn (or at least determine Δn as being one of two values). The present inventor has realised that knowing λi (or λ₂), δλ and Δn means it is then possible to calculate accurately the distance D_ex. In the particular systems described herein with reference to Figures 1 , 6 & 7, an interferometer is utilised to determine the distance relative to the object. An interferometer is basically a differencing system i.e. it finds the differences in two optical path lengths. Sections within the interferometer along which both beams travel on the same path will not contribute to the difference in optical path length, and hence will drop out of the calculation. Thus, with reference to Figure 1, the path 30 between the radiation source 10 and the beam splitter 16, and the common path 34, 38 followed by both beams from the beam splitter 16 to the imaging screen 18, will both not contribute to the distance measurement. The beam splitter 16 splits the single beam incident along path 30 into two beam portions, one of which is directed along the path 32 towards reflective surface 14, and the other of which is directed along path 36 towards reflective surface 12. Each of these beam portions is reflected from a respective reflective surface 12, 14 back to beam splitter 16. As previously mentioned, the point of interference of the two beam portions is actually at the beam splitter 16, although the interference pattern is not actually displayed/measured until it is incident on screen 18. Thus, the actual distance being measured in the embodiments described with reference to Figures 1, 6 & 7 is the relative distance between reflective surfaces 12 & 14, along the optical beam paths. In other words, it is D, where D = D_ref + D_meas, where D_ref is the distance from the reflective surface 14 to the beam splitter 16 along the beam path (32), and D_meas is the distance from the beam splitter 16 to the reflective surface 12 along the beam path (36).

In most practical implementations, the apparatus will be configured such that the distance from the beam splitter 16 to one of the reflective surfaces (e.g. reflective surface 14) is fixed (e.g. D_ref is a fixed, known value). Thus, the distance from the beam splitter 16 to the other reflective surface (e.g. reflective surface 12) can be easily calculated (D_meas = D - D_ref) once the relative distance D between the two reflective surfaces 14, 12, along the optical beam path, has been calculated.

Further explanation of the technique for calculating the phase difference between the two interference patterns obtained by using the two different wavelength radiation beams will now be provided.

A cross-section of the intensity pattern at the output of the interferometer (i.e. the intensity of the interference pattern) of the device illustrated in Figure 1 is illustrated in Figure 4, the device operating using a first beam of first wavelength λi. The interference fringes 181 correspond to peaks in the intensity pattern. The interference fringes are of separation d. As indicated previously, the interference fringes contour the interval λ_\/2. A point within the image is selected, which in the example shown corresponds to the maxima of a bright fringe, denoted Φ_\. It should be noted that it is not generally possible to determine the actual phase of the beam at that point, as the fringe pattern extends infinitely in all directions, and no datum point is known at which the phase is zero; hence Φ_\ is effectively undefined. The wavelength of the laser source is then changed by δλ to a new value λ₂. In this particular example, δλ is chosen to be positive and hence:

A₂ = A₁ + δλ (4)

The output of the interferometer will, to most general appearances, remain substantially the same. Figure 5 illustrates the corresponding interference pattern

180'. Again the interference pattern appears as a series of fringes, having intensity peaks 181'. However, the spacing of the intensity peaks will have changed i.e. the spacing is now d', as the fringes contour the interval λ₂/2. Further, the pattern will have experienced a phase shift owing to the new number of waves (i.e. n₂) occupying the distance D. This situation is illustrated in Figure 5, in which Φ₂ indicates the same physical position at the interferometer output as Φi. As for Φi, the value of the phase at Φ₂ is not known.

Typically, the difference between these two phase values will be relatively large e.g. if D is around 0.5 metres, λ_\ 650nm, and δλ O.lnm, then the shift, in cycles or waves between the two examples illustrated in Figures 4 and 5 could be calculated by:

where, Δn is the difference in the number of waves over the distance D.

Calculating this difference using the above values gives a value of Δn of 118.325 waves or cycles.

In general, the relationship between the two phases can be written as O₂ = O₁ -I- 2πAN + δφ (6) where ΔN is the whole number (integer) portion of Δn and δ φ is the fractional portion e.g. ΔN = 118 and δφ = 0.325 (or approximately 2.04 radians) in this example.

Whilst it is generally not possible to know the phases O₁ , and Φ₂ at the two different points, it is possible to know the relative phases of the interference patterns.

For example, Fourier transform fringe analysis can be used to determine the phase fields in the output images from the Michelson interferometer, and hence δ^ calculated. FTFA analyses fringe patterns to determine relative phase data. The analysis of each image will not yield the true absolute phase value, but will, by calculating the difference between the phase values at the same position in each image, determine the difference between the two phases i.e. the fractional fringe shift δ^ . Applying equation (1), in a slightly rearranged form, to the second Michelson image leads to

D = N₁X₁ (7)

2π where N₂ is the whole number of waves in the distance D in the case of illumination from a radiation beam of wavelength λ₂, and δφ is the fractional part of the wave over the same distance. Substituting using equations (3) and (4) provides:

which reduces to:

Equations (1) and (9) constitute two equations in three unknowns - namely D, n_t and ΔN. It is therefore possible to generate more equations by simply taking more wavelength steps of δλ. In other words, in a more general form, equation (9) can be expressed as: D = H₁ - AN₁₁ + (λ_λ + kδλ) (10)

2π

where ni is the number of waves in the distance D at wavelength λi

ΔN_k is the integer change in the number of waves between λi and λ_k δ φ _k is the incremental phase shift observed for a radiation beam of λ_k relative to the starting, or initial, radiation beam of wavelength λ_\ , δλ is the constant incremental wavelength step in each case.

It should be noted that if k = zero, then equation (10) reduces to a simple rearrangement of equation (1) - i.e.

D = H₁A₁ (11),

thus showing that it is indeed the most general form of relationship to the case of varying wavelength.

Equation (10) can then be used to generate a set of (k + 1) equations in (k + 2) unknowns - viz; D, n_l5 and ΔN, ... ΔN_k. This set can be solved by rearranging equation (10) into the form: δφ_

D - _n] - AN_k + ^ {λ_ι + kδλ) = Q (12).

2π

The sign information can be removed by squaring both sides; summing the residual over all cases of the equation provides:

(I₁ + kδλ) = ε => min (13)

This solution can be assisted by placing appropriate constraints upon the solution space.

In particular, these constrains can originate from the fact that an approximate value of D is already known.

By way of example, assume that distance D_approx is known to within an error +ΔD of lOμm, and is approximately 0.5m. Consider the first wavelength to be 650nm, and the second wavelength to be 650. lnm. This provides the following constraints:

1. 0.49999 < D_approx < 0.50001

D D

2. The minimum and maximum values of ni ' are n. l mi .n = — o ⁵^⁵- and n. l max = — o ^- ,'

A₁ A₁ giving 769215 < n < 769246

3. finally, the situation with the ΔN^ terms is more complex but the limits for the ΔN term can be calculated as;

giving 118 < Δn < 120 i.e. the integer ΔN is either 118 or 119.

As Δn is known to be either 118 and a fraction or 119 and a fraction, then the integer value ΔN must be either one of the integers 118 or 119.

This result arises because the value of D is already known to within predetermined limits, and also because the difference between the two wavelengths is relatively small (i.e. just 0. lnm).

As the nominal wavelength is 650nm, when the radiation source output is changed to 650. lnm, it will take a train of 6500 waves for the new wavelength to gain one cycle on the old wavelength - and under typical conditions 6500 waves is well over 4mm in length. As D is known to within a value of 20 μm there will only ever be one cycle change within that length - there cannot be two, as the length is not long enough to accommodate such cycle changes. Thus, in order to realise ΔN to within unity, D does not need to be known to the precision of 20μm.

In fact, denoting the initial uncertainty (error) in the approximate measurement of D as ΔD, the allowable error in the approximate measurement is: λ²

± AD < (14)

2δλ (Appendix 1 illustrates how this equation (14) can be derived).

This implies that the allowable error in the approximate measurement of D is, in this particular example, 2.114mm. Such an error would still allow the values of N^ to be known to within one.

Using equation (1) to substitute into equation (9) gives:

D = ^2D A ΛNΛΓ + — ^δΦ (X_{1 +} SX) (15), λ_λ 2π

which rearranges to:

Using equation 16, an accurate value for D can be calculated. The left hand side contains only D - the desired end result of our analysis. The right hand side includes terms for the wavelength, the difference in wavelength, the phase difference

60, and ΔN (which is known to be an integer, and its value is known within unity).

Substituting in turn both of the two permitted values of ΔN in equation (16) (i.e. attempting to utilise both 118 and 119) will lead to two initial values for D. The correct value of D will be the only value that is with inside the error range of the initial approximate measurement.

By appropriate selection of the two wavelengths it is possible to configure the uncertainty range - i.e. the range within which N (or in other words, ΔN as it is referred to above) will change by unity, in such a way that it exactly matches the uncertainty in the measured value D. Suppose that the precise value of D is given by ΔL' and this is estimated with an error of ε, then the following can be ensured;

ΔL' - ε = Nλ_s (16a) and ΔL' + ε = (N + l)λ_s (16b)

where A_s = ^ That is the distance over which N (or in other words, ΔN as it is referred to above) changes by unity and exactly aligns with the distance uncertainty and furthermore the value would be exactly N at the start of the range and exactly N+l at the end. If the resultant fringe patterns from the interferometer are now captured for these two wavelengths and the fractional phase shift f_t is determined, then a new more accurate estimate of ΔL' (referred to as ΔL'_X), is given by:

ΔL'_t = ΔL' + XJ₁ (16c)

This fractional phase shift, Z₁, is the phase difference between the two images, resulting from the two discrete wavelengths, taken modulo 2π. In practice the finite size of the stable tunability steps of the laser make it difficult or impossible to totally satisfy equations (16a) and (16b). However experiment confirms that it is possible to be sufficiently close to satisfying equations (16a) and (16b) so as to make this approach fully practical.

Assuming that f_\ can be determined to an accuracy of better than λ_s/10, readily achievable using a phase measurement technique such as Fourier transform fringe analysis, it can be concluded that the new estimate of the distance, ΔL'j is ten times better than the starting estimate, ΔL'. That is to say the true distance can be described as: (ΔLj — ε/10) < ΔL < (ΔL'j + ε/10). The process can now be used again, this time using ΔL'_A as the initial estimate and ±ε/10 as the uncertainty. In general equation (16c) can be written as:

ΔL'_C+1 = ΔL'_S + λ_Sjf_i+1 (16d)

It will be understood that ever more accurate estimates of the distance can be obtained, each one ten times more accurate than the last. Starting with, say ε =lmm, μm levels of precision could be reached within three iterations of the process. The accuracy of this method is ultimately limited by the tuning range of the laser. However, modern narrow bandwidth tunable lasers have a nominal tuning range of approximately 7-8nm about a centre-point wavelength of 680nm, and this would allow λ_s values as small as 40μm and associated accuracies in ΔL'_i+1 of the order of 4μm.

The technique described above only requires two images to be captured and analysed, and one wavelength shift known or measured, to provide an accurate distance measurement. As can be seen by reference to equation (14), generally the smaller wavelength difference δλ between the two radiation beams, the better. For example, preferably δλ< 5nm, or even δλ<lnm, or δλO.lnm. Typically δλ will be less than λi /100, or even less than λi/1000 or λi/lOOOO.This is in contrast to prior art techniques, in which δλ is preferably as large as possible. Thus, lasers can be utilised that can tune only over a narrow wavelength range, allowing relatively cheap radiation sources to be utilised. Alternatively, as the fringes need not be continuously observed over the tuning range, two discrete wavelength sources could be utilised, each providing a separate wavelength. Further, from equation (14), it will also be appreciated that generally the longer the wavelength, the better i.e. the less accurate the approximate measurement of D needs to be. This fits well with cheap commercially available radiation sources such as laser diodes.

In prior art techniques using wavelength — sweeping techniques for distance measurement, it is desirable that a large number of fringes pass the detector, and so to maximise the accuracy of detection, it is desirable that ΔN is relatively large. For example, it is believed that typically values of ΔN for such wavelength sweeping devices would be of the order of 100000. Such large ΔN values are achieved by using relatively large wavelength differences between the two extreme wavelengths used in the measurement (i.e. a relatively large δλ). In contrast, in embodiments of the present invention, Δ N values would typically be a lot smaller e.g. typically in the range 100-2000, and generally less than 10000.

It should be appreciated that the above implementation is described by way of example only, and that various alternatives will be apparent to the skilled person, as falling within the scope of the present invention. For example, the technique described herein could be implemented by using a variety of interferometry, signal heterodyning or similar methods. Two further embodiments of the present invention will now be described with reference to Figures 6 & 7.

Figures 6 & 7 show modified interferometer apparatus, which are based upon the device 100 illustrated in Figure 1. Identical reference numerals within the Figures are utilised to show similar features.

The device 100' illustrated in Figure 6 is generally similar to that illustrated in Figure 1 , but with the addition of an optical element 40 in the beam path between the beam splitter 16 and imaging screen 18. The optical element 40 is used to expand the diameter of the incident radiation beam. The incident radiation beam is actually a composite beam formed of a beam portion reflected from reflected surface 14 and a beam portion reflected from reflective surface 12, and will thus contain interference fringes. The beam diameter will typically be between 0.1 and 1.0 mm. The optical element 40 will expand the beam to any suitable diameter for display on the imaging screen 18. For instance, the optical element 30 may expand the beam up to 50mm, although this beam diameter could be larger depending on the size of the optics used to expand and accommodate the beam.

For example, the optical element 40 could be a lens, or a group of lens. The diameter of the radiation beam is expanded so as to enhance the visibility of the interference fringes formed within that beam, and so as to make the fringes easier to detect (and to be seen by the naked eye).

Typically, the mirror tilt θ will be chosen so as to ensure that around 20-30 fringes are displayed across the imaging screen 18.

The apparatus 100' illustrated in Figure 6 can be used to make a distance measurement in the same manner as described with reference to the apparatus in Figure 1. Equally, the apparatus illustrated in Figure 1 & 6 can be utilised in a slightly different manner, so as to select an optimum value of δλ i.e. the difference between the two wavelengths (λj λ₂) used to make the distance measurement. This method will now be described in more detail.

Firstly, the distance D is estimated or roughly measured, so as to provide a value D_approx i.e. the approximate distance is determined from the reflective surface

14, along the beam path 32 to the beam splitter 16, and from the beam splitter 16 to the reflective surface 12. Based upon the measurement technique utilised, this approximate distance D will have a corresponding uncertainty or error (±ΔD). In other words, the distance D = D_approx + ±ΔD. Based upon this error or uncertainty in the D measurement or estimation, the maximum difference between the two wavelengths (λi λ₂) can be estimated:

[This maximum value for the permissible change in wavelength, δλ_max, is derived in Appendix 1).

This value of δλ_aax is the largest change in wavelength that can be used, and for which we can be sure of only obtaining two possible integer values of ΔN. If the wavelength change (δλ) is larger than the calculated value of δλ_maX, then there could be three or more possible values of ΔN. Alternatively, if the wavelength change δλ is less than half the value of δλπ,_aχ₅ whilst this could result in only being one permissible value for ΔN, this could potentially compromise the precision of the measurement.

Consequently, it is most desirable to select a value of δλ somewhere between δλ_max and δλ_maχ/2. Thus, the change in wavelength is effectively matched against the uncertainty in the distance measurement/estimate. For example, if λl=685nm and

ΔD=lmm then the preferred value δλ would be given by:

0.12nm<δλ <0.24nm (18)

As tunable lasers are readily available that can achieve reliable, stable, wavelength changes of fractions of nanometres (e.g. down to 0.000 lnm or less), the condition indicated in relationship (18) is readily obtainable.

As previously, first and second images of the interference fringes are captured, with each image corresponding to the image formed by a respective wavelength (λi λ₂), where λ₂ = λi + δλ). As previously, FTFA (Fourier transform fringe analysis) can then be utilised to determine the change in phase between the two interference patterns i.e. δφ.

The two possible integer values of ΔN are then calculated, using:

(19)

£> and ΔiV, = A*

K ΔD

+ ΔD

These two values of ΔN are then substituted into:

D =^^Α__AN (20) δλ \ lπ to yield the accurate value of D.

The above described technique is particularly suitable for measuring distances relative to a particular point on an object i.e. the position in which the beam portion 36 is incident on the object, if the objects acts as reflective surface 12, or the position at which the beam portion 32 is incident on the object, if the object acts as reflective surface 14. If it is desirable to form a topographic profile of an object, then the method can be repeated for a variety of different predetermined paths to the object, so as to calculate the distance to different positions on the object, and hence determine the topographic profile.

Alternatively, as will now be described with reference to Figure 7, an expanded beam (or relatively wide beam) can be utilised, so as to determine the distance to a number of different points (all within the area used to reflect the beam) on the object.

The device 200 illustrated in Figure 7 is broadly similar to the device 100 illustrated in Figure 1.

As previously, a radiation source 10 is used to provide two main beams of radiation, of separate wavelengths λi, λ₂ at different times. Each wavelength will result in the formation of a respective interference pattern on imaging screen 18. In this embodiment, the device 200 is arranged to utilise two relatively large diameter beams (e.g. radiation beams having a diameter of between 0 and 500mm, and typically around 50mm for cost considerations related to the cost of optical elements for expanding and accommodating the beam) to form the interference pattern. Such relatively large diameter, collimated beams are formed by a beam expander 240. The beam expander 240 is located in the optical path between the radiation source 10 and the beam splitter 16, and is used to expand the collimated radiation beam output from the radiation source into a larger diameter, but still collimated, radiation beam 130. The beam expander 240 can be formed in any number of ways, but in the example shown consists of two optical lenses, one arranged to expand the beam and the other arranged to collimate the resulting expanded beam.

The path of the radiation beam 130 through the beam splitter 16, and reflecting from the reflective surfaces 12, 14 is generally the same as the path of the unexpanded beam and beam portions through the beam splitter, as described with reference to Figure 1. Hence the beam paths are indicated by similar reference numerals, but prefixed by the letter 1 (i.e. path 132 corresponds to path 32 etc).

In the embodiments shown in Figure 1, due to the relatively narrow width of the radiation beam, the object could be envisaged as simply being illuminated at a single point (i.e. reflection occurs from a relatively small area of the object). In this particular embodiment however, due to the larger diameter of the radiation beam 130 (and consequently, the large diameter of the corresponding radiation beam portions 132 & 136), a larger portion of the object area will be illuminated (and reflect the incident radiation beam).

As previously indicated, either reflective surface 12 or reflective surface 14 could act as the reference arm of the interferometer, with the other arm acting as a measurement arm. In this particular embodiment, it is preferable that the reflective surface 12 acts as the reference arm i.e. that the reflective surface having a predetermined tilt relative to the perpendicular to the incident radiation beam (the tilt being angle θ), is used as the reference reflective surface. Thus, the object in Figure 7 would be represented by reflective surface 14, so as to easily allow the determination of the different distances D from the corresponding portions/positions reflective surface 12 to the different portions/positions of reflective surface 14. The device 200 will effectively measure the distance from each point on the reference mirror/reflective surface 12 to a corresponding point on the object/target reflective surface 14, with a one-to-one mapping. As the reference reflective surface 12 is tilted, this introduces a systematic change in length at different positions across the mirror 12. The angle θ is therefore measured, such that the effect of this change on lengths D across the reflective surface 12 can be subtracted from the determined lengths. In other words, due to tilt θ, the distance D_ref will vary (i.e. the distance between the beam splitter 16 and the reflective surface 12, in this embodiment) across the mirror 12. Thus for each calculated value, D_ref needs to be known such that O_meas (i.e. the distances from the beam splitter 16 to the positions on the reflective surface 14) can be calculated. The distance D_meas can thus be calculated at a number of different positions across the radiation beam profile. Prior to use, the apparatus shown in Figure 7 would first be calibrated, and the angle θ of the reference reflective surface 12 calculated. This can easily be done by introducing a planar mirror into position 14 (this position is later occupied by the reflective surface of the object e.g. the remainder of the apparatus could be moved to a position relative to the object at a later time, with the mirror in that position 14 having been removed). The mirror in the position of reflective surface 14 would be a planar mirror extending perpendicular to the incident reflected beam 32. Firstly, the interferometer is set into infinite fringe mode i.e. with no tilt on the reference reflective surface 12 (which, for simplicity, is preferably a planar mirror). The planar mirror 12 is then tilted so as provide between 25 and 30 fringes across the image of the interference pattern formed on the imaging screen 18. Assuming that the number of fringes visible across the imaging screen 18 is n_f, then knowing the magnification factor of the detector system it can be calculated that are n_f fringes in a detector width of D_w. As the fringes represent changes in path length of λ/2, where λ can be either the first wavelength or the second wavelength, then the angle of tilt of the mirror can be determined from:

A single point measurement method can then be carried out at each pixel on the imaging screen 18, or at any desired combination of pixels, by applying a correction for the tilt of the planar mirror 12 as xtan(θ), where x is the horizontal image coordinate relative to the image centre (i.e. x - 0 at the image centre). Thus, by again successively providing two different beams of radiation, and analysing the resulting phase change at different points on the fringe patterns displayed on the imaging screen 18, the variation in phase between the two different wavelengths can be determined, and hence the distance D calculated for each point. The distance D_meas from the beam splitter 16 to each point on the object at position 14 can thus be determined, across the width of the radiation beam portion 32.

In accordance embodiments of the present invention, a method of determining a distance relative to an object has been described. Although not explicitly described, it will be appreciated that the embodiments described thus far have related to the determination of a distance relative to a stationary object. In accordance with a further embodiment of the present invention, a method of determining a distance relative to a moving object may be undertaken. The method may be as described above, and may be repeated on one or more occasions to obtain one or more distances relative to the moving object. If the method is repeated on more than one occasion, a dynamic determination of the distance may be obtained.

Appendix 1 Derivation of the Uncertainty Tolerance Relationship Equation (14)

The relationship giving the change in number of cycles for the minimum (D_mi_n) and maximum (D₁,^) length conditions is;

£L, . D,

And N, =

K

ΔN (=(N1-N2)) should be unity, i.e.

Or

Which rearranges to δX

X₁X₂ (Anax -AninH

Therefore δλ

(D + AD - (D -AD ))= I

X_xX₂ So δX =

2AD

If δλ is small, then

and the permissible change in wavelength to ensure a difference in N of unity for a given uncertainty in D, ΔD can be calculated as:

δX_^ = ^■ Λ²

2AD

Claims

1. A method of determining a distance relative to an object, comprising: determining the phase difference between a first beam of radiation of a first wavelength incident on an object along a predetermined path, and a second beam of radiation of a second, different wavelength incident on the object along the predetermined path; determining the difference between the first and second wavelengths; calculating the distance relative to the object utilising the determined phase difference, the determined wavelength difference, the value of one of said wavelengths, and an approximate distance relative to the object.

2. A method as claimed in claim 1, wherein the approximate distance relative to the object is known to within an accuracy of ± ΔD , where

± ΔD < V₂

2δλ ' where δλ is the difference between the two wavelengths, λ_\ is the first wavelength and λ₂ is the second wavelength.

3. A method as claimed in any one of the above claims, wherein the phase difference is determined at a plurality of different positions across the width of said path, and the distance relative to the object is calculated for each of said positions.

4. A method as claimed in any one of the above claims, wherein the phase difference between the radiation beams is determined by: analysing a first interference pattern formed from a portion of the first beam of radiation reflected from the object; analysing a second interference pattern formed from a portion of the second beam of radiation reflected from the object; and comparing the analysis of the first interference pattern with the second interference pattern.

5. A method as claimed in claim 4, wherein the interference patterns are analysed using Fourier transform fringe analysis.

6. A method as claimed in any one of the above claims, further comprising: calculating the maximum and minimum values for the difference Δn between the number of waves of the first radiation beam along the predetermined path, and the number of waves of the second beam of radiation along the predetermined path, based upon the wavelengths of the radiation beams and the maximum and minimum possible values of the approximate distance.

7. A method as claimed in any one of the above claims, further comprising calculating the value of a parameter D indicative of the distance relative to the object,

where λ_\ is the wavelength of the first radiation beam, δλ is the difference in wavelength between the two radiation beams, δ φ is the determined phase difference, ΔN is an integer difference in the number of waves of the first radiation beam along the predetermined path and of the second radiation beam along the predetermined path.

8. A method as claimed in claim 7, wherein the values of D are calculated for the values of ΔN determined using claim 6, the value of D falling between the maximum and minimum possible values of the approximate distance being determined as the actual distance.

9. A method of measuring a distance relative to an object, comprising: providing a first beam of radiation incident on the object along a predetermined path; and providing a second beam of radiation of a second, different wavelength incident on the object along the same path; and performing the method as claimed in any one of claims 1 to 8.

10. A method as claimed in claim 9, further comprising measuring the approximate distance relative to the object.

11. A method as claimed in claim 9 or claim 10, wherein the object is at least partially reflective.

12. A method as claimed in any one of claims 9 to 11, wherein the object is a mirror placed a predetermined distance from a further object, the method further comprising determining the distance to the further object based upon the predetermined distance and the calculated distance relative to the object.

13. A method as claimed in claim 10 or any claim dependent thereto, wherein the approximate distance relative to the object is measured within an error of ±ΔD, and the maximum difference in wavelength between the second wavelength and the first

wavelength λi is calculated by — — .

14. A method as claimed in claim 13, further comprising selecting the wavelength of the second radiation beam such that the different δλ between the first wavelength and the second wavelength satisfies the relationship δλ_maχ/2 < δλ < δλ_max.

15. A method as claimed in any one of claims 9 to 14, wherein said beams are incident on the object on a surface of the object extending transverse, but not perpendicular to, the predetermined path.

16. A method as claimed in any one of claims 9 to 15, further comprising: forming an interference pattern between a reflected portion of the first radiation beam and a respective reference beam; forming an interference pattern between a reflected portion of the second radiation beam and a respective reference beam; and determining the phase difference from said interference patterns.

17. A method as claimed in claim 16, wherein said reference beams are both directed along a predetermined reference path and reflected from a surface of a reference mirror.

18. A method as claimed in claim 17, wherein the reference mirror extends transverse, but not perpendicular to, the path of the incident reference beams.

19. A method as claimed in claim 15 or 18, wherein at least one of the surfaces is planar.

20. A method as claimed in claim 17 or any claim dependent thereto, wherein the first radiation beam and the respective reference beam are formed from a first main beam split by a beam splitter, and the second radiation beam and the respective reference beam are formed from a second main beam split by a beam splitter, the relative distance being the total distance along the beam path from the surface of the reference mirror to the beam splitter, and from the beam splitter to the object.

21. A method as claimed in any one of claims 16 to 20, wherein said interference patterns are formed on the input of an image capture device arranged to capture an electronic image of each interference pattern for analysis thereof.

22. A method of forming a topographic profile of an object, comprising: performing the method as claimed in any one of claims 1 to 21, for a variety of different predetermined paths to different positions on the object; and calculating a topographic profile for the object based upon the relative distance calculated for each path.

23. A method of forming a topographic profile of an object, comprising: performing the method as claimed in claim 3 or any claim dependent thereto; and calculating a topographic profile for the object based upon the relative distances calculated for each of said positions.

24. A method as claimed in any of claims 1 to 21, wherein a distance relative to a moving object is determined.

25. A method as claimed in claim 24, wherein a dynamic measurement of the distance relative to the moving object is determined by repeating the method.

26. A carrier medium carrying computer readable program code configured to cause a computing device to carry out a method according to any one of claims 1 to 25.

27. A device for controlling an interferometer to carry out a distance measurement, the device comprising: a program memory containing processor readable instructions; and a processor configured to read and execute instructions stored in said program memory; wherein said process readable instructions comprise instructions configured to control said device to carry out a method according to any one of claims 1 to 25.

28. A device for determining a distance relative to an object, the device comprising: a radiation source for providing a first beam of radiation of a first wavelength, and a second beam of radiation of a second, different wavelength incident on the object along the same path; a measurement device to determine the phase difference between the first beam of radiation incident on the object and the second beam of radiation incident on the object; a computational device arranged to carry out the method of any one of claims 1 to 25.

29. A device as claimed in claim 28, wherein the difference in wavelength between the two beams is less than 5nm.

30. A device as claimed in claim 28 or claim 29, wherein the device comprises an interferometer.