WO2017216581A1

WO2017216581A1 - Lidar

Info

Publication number: WO2017216581A1
Application number: PCT/GB2017/051770
Authority: WO
Inventors: Matthew S. WARDEN
Original assignee: Fraunhofer Uk Research Ltd
Priority date: 2016-06-16
Filing date: 2017-06-16
Publication date: 2017-12-21
Also published as: GB201610523D0

Abstract

A method for determining range and velocity information for a collection of moving scatterers comprises frequency modulating and/or phase modulating continuous wave light to form a modulated signal beam. The method comprises transmitting the modulated signal beam to the collection of scatterers, detecting light back-scattered by the collection of scatterers, and analysing the detected signal using a matched filter to provide range and velocity information for the collection of scatterers. The scatterers may comprise atmospheric aerosols. The system may be used to provide a measure of wind speed and/or a measure of air turbulence.

Description

Lidar

Field of the Invention

The present invention relates to a system and method for measuring the joint range - velocity distribution of a collection of light scatterers using frequency and/or phase modulation continuous wave lidar.

Background of the Invention

Doppler lidar is used to make remote measurements of wind speed. This is used, for example, to help plan the location of wind farms, to monitor how well a wind turbine performs in different wind conditions, or for real time monitoring of wind conditions that may be fed back to a wind turbine to improve its performance. Doppler lidar may also be used to measure the air turbulence created by aircraft or vehicles, and for wind tunnel testing. The operating principle of Doppler lidar is as follows. A laser beam is transmitted through a volume of air to be measured. Some of the light from this beam is back- scattered by atmospheric aerosols and is detected by the Doppler lidar. The atmospheric aerosols move with the same velocity as the wind. In general, these aerosols have a component of motion, known as the line of sight velocity, in a direction collinear with the laser beam. In general, the back-scattered light has an optical frequency that is different from the optical frequency of the transmitted beam. This frequency difference, known as the Doppler shift, is proportional to the line of sight velocity with a known constant of proportionality. The frequency difference is measured by the lidar. The measured frequency difference and known constant of proportionality are used to infer the line of sight velocity.

Commonly used Doppler lidar systems may be grouped into two types: continuous wave Doppler lidar, and pulsed Doppler lidar. Continuous wave Doppler lidar typically transmits a laser beam that is focussed at some desired range away from the lidar. The back-scattered light from the region near the focus of the beam results in a stronger signal in the lidar detector. Therefore, the line of sight velocity that is measured is due predominantly to the wind around the location of the beam focus. This effect is used to fix the range at which a continuous wave Doppler lidar measures. Continuous wave Doppler lidar can only measure the line of sight velocity of the wind at one range at any one time. The line of sight velocity may be measured at different ranges sequentially by adjusting the focus optics. However, the adjustment takes time and requires bulky moving parts. With continuous wave Doppler lidar the range resolution of the measurements increases (worsens) for longer measurement ranges, as the beam focus becomes more elongated. In addition, continuous wave Doppler lidar suffers from measurement errors if a strong scatterer, such as a cloud, is present near the lidar beam focus. Pulsed Doppler lidar emits light in short pulses. Light scattered at different ranges from the lidar reaches a detector at different times allowing for the measurement of line of sight velocity at many different ranges. The pulses can be considered as amplitude modulated light. The pulses in pulsed Doppler lidar require a high peak power, which increases the cost of system components as they must be able to handle this power. This also means that the average power of pulsed Doppler lidar is lower. Therefore, pulsed Doppler lidar takes longer to make a measurement as it must average over many pulses in order to improve the signal to noise ratio.

As is well known, there is a trade-off between range resolution and the line of sight velocity resolution for pulsed Doppler lidars. Increasing one decreases the other, so that it is not possible to improve both simultaneously with conventional methods. The range and velocity resolution of pulsed Doppler lidars is closely related to the shape of the emitted pulses. It is technically challenging to optimise this. Summary of the Invention

It should be understood that any one or more of the features of the following aspects or embodiments may apply alone or in any combination in relation to any of the other following aspects or embodiments. According to an aspect or an embodiment there is provided a method for determining range and velocity information for a collection of moving scatterers comprising:

frequency modulating and/or phase modulating continuous wave light to form a modulated signal beam;

transmitting the modulated signal beam to the collection of scatterers;

detecting light back-scattered by the collection of scatterers, and analysing the detected signal using a matched filter to provide range and velocity information for the collection of scatterers.

By using frequency modulated continuous wave light or phase modulated continuous wave light as the signal beam, different ranges and velocities can be sensed in a single measurement at a return signal power level that provides adequate resolution.

The method may comprise frequency modulating continuous wave light so that the modulated signal beam comprises a frequency modulated signal beam. The frequency modulated signal beam may comprise more than two slopes.

The frequency modulated signal beam may comprise multiple linear sections. The frequency modulated signal beam may comprise multiple linear sections each with a different gradient. The frequency modulated signal beam may comprise at least three linear sections each with a different gradient. Analysing the detected signal using a matched filter may involve analysing the detected signal corresponding to each linear section using a Fourier transform.

The frequency modulated signal beam may comprise a triangular waveform.

The frequency modulated signal beam may comprise multiple triangular waveforms. Each triangle may have the same duration but a different height. The height may increase as a function of time. The height may decrease as a function of time. Each triangle may be of the same height but a different duration. The duration may increase as a function of time. The duration may decrease as a function of time.

The frequency modulated signal beam may comprise a sinusoidal waveform.

The method may comprise using a reference beam that is substantially the same as the frequency modulated signal beam.

The method may comprise monitoring the frequency of the frequency modulated signal beam and using the monitored frequency in the matched filter analysis. The method may comprise phase modulating continuous wave light so that the modulated signal beam comprises a phase modulated signal beam.

The phase modulated signal beam may comprise a binary coded phase modulation waveform which varies between two binary values. The two binary values may differ by 180 degrees. The binary coded phase modulation waveform may comprise a pseudo-random binary sequence. The binary coded phase modulation waveform may comprise a binary Barker code. The phase modulated signal beam may comprise a polyphase coded modulation waveform which varies between more than two discrete values. The polyphase coded modulation waveform may comprise a polyphase Barker code.

The modulated signal beam may comprise a substantially collimated beam of light.

The range and velocity information may comprise a range-velocity profile or map.

The scatterers may comprise atmospheric aerosols. The method may comprise using the range and velocity information for the collection of scatterers to provide a measure of wind speed.

The method may comprise using the range and velocity information for the collection of scatterers to provide a measure of air turbulence.

According to an aspect or an embodiment there is provided a system for determining range and velocity information for a collection of moving scatterers, the system being configured to:

frequency modulate and/or phase modulate continuous wave light to form a modulated signal beam;

transmit the modulated signal beam to the collection of scatterers;

detect light back-scattered by the collection of scatterers; and

analyse the detected signal using a matched filter to provide range and velocity information for the collection of scatterers. The system may be configured to frequency modulate continuous wave light so that the modulated signal beam comprises a frequency modulated signal beam. The frequency modulated signal beam may comprise more than two slopes. The frequency modulated signal beam may comprise multiple linear sections. The frequency modulated signal beam may comprise multiple linear sections each with a different gradient. The frequency modulated signal beam may comprise at least three linear sections each with a different gradient. Analysing the detected signal using a matched filter may involve analysing the detected signal corresponding to each linear section using a Fourier transform.

The frequency modulated signal beam may comprises a triangular waveform.

The frequency modulated signal beam may comprise multiple triangular waveforms. Each triangle may have the same duration but a different height. The height may increase as a function of time. The height may decrease as a function of time. Each triangle may be of the same height but a different duration. The duration may increase as a function of time. The duration may decrease as a function of time. The frequency modulated signal beam may comprise a sinusoidal waveform.

The system may be adapted to use a reference beam that is substantially the same as the frequency modulated signal beam. The system may be adapted to monitor the frequency of the signal beam and use the monitored frequency in the matched filter analysis.

The system may be configured to phase modulate continuous wave light so that the modulated signal beam comprises a phase modulated signal beam.

The system may comprise a collimator for collimating the modulated signal beam.

The range and velocity information may comprise a range-velocity profile or map. The scatterers may comprise atmospheric aerosols.

The system may be adapted to use the range and velocity information for the collection of scatterers to provide a measure of wind speed. The system may be adapted to use the range and velocity information for the collection of scatterers to provide a measure of air turbulence.

According to an aspect or an embodiment there is provided a method for determining range-velocity information for a collection of moving scatterers comprising:

frequency modulating continuous wave light using a modulating pattern to form a frequency modulated signal beam;

transmitting the frequency modulated signal beam to the collection of scatterers;

detecting light back-scattered by the collection of scatterers, and

analysing the detected signal using a matched filter to provide range and velocity information, for example a range-velocity profile or map, for the collection of scatterers.

By using frequency modulated continuous wave light as the signal beam, different ranges and velocities can be sensed in a single measurement at a return signal power level that provides adequate resolution.

The frequency modulated signal beam may contain more than two slopes.

The signal beam may be a substantially collimated beam of light. The frequency modulated signal beam may comprise multiple linear sections. The frequency modulated signal beam may comprise multiple linear sections each with a different gradient. The frequency modulated signal beam may comprise at least three linear sections each with a different gradient.

Where the frequency modulated signal beam comprises multiple linear sections, analysing the detected signal using a matched filter may involve analysing the detected signal corresponding to each linear section using a Fourier transform. A fast fourier transform could be used, thereby to increase the speed of the analysis.

The frequency modulated signal beam may comprise at least one triangular waveform. The frequency modulated signal beam may comprise multiple triangular waveforms.

Where the frequency modulated signal beam comprises multiple triangular waveforms, each triangle may be of the same duration but different heights. The height may increase as a function of time. Alternatively, the height may decrease as a function of time.

Where the frequency modulated signal beam comprises multiple triangular waveforms, each triangle may be of the same height but different durations. The duration may increase as a function of time. Alternatively, the duration may decrease as a function of time.

The frequency modulated signal beam may comprise a sinusoidal waveform or multiple sinusoidal waveforms. Each sinusoidal waveform comprises multiple different slopes of different gradient (in particular more than two different slopes with different gradients). Using a sinusoidal waveform simplifies the methodology, as in general such waveforms are easier to generate than for example triangular waveforms.

The method may involve using a reference beam that is substantially the same as the frequency modulated signal beam. The method may involve monitoring the frequency of the signal beam and using the monitored frequency in the matched filter analysis.

The scatterers may comprise atmospheric aerosols.

The method may involve using the range-velocity profile for the collection of scatterers to provide a measure of wind speed.

According to an aspect or an embodiment there is provided a system for determining range-velocity information for a collection of moving scatterers, the system being adapted to:

frequency modulate continuous wave light using a modulating pattern to form a frequency modulated signal beam;

transmit the frequency modulated signal beam to the collection of scatterers; detect light back-scattered by the collection of scatterers, and

analyse the detected signal using a matched filter to provide range and velocity information, for example a range-velocity profile for the collection of scatterers.

Brief Description of the Drawings

Various aspects of the invention will now be described by way of example only and with reference to the accompanying drawings, of which:

Figure 1 is a schematic view of a frequency modulated continuous wave Doppler lidar system;

Figure 2 is an illustration of line of sight velocity and range of a scatterer;

Figure 3 is a flow chart of an analysis algorithm based on a matched filter for use with the lidar system of Figure 1 ;

Figure 4 is a collection of illustrations of example frequency modulation patterns for use in the lidar system of Figure 1 ;

Figure 5 is a flow chart of another example of a matched filter based analysis algorithm;

Figure 6 is plot showing the relationship between a measured signal and a range - velocity power distribution;

Figure 7 is a plot of a range-velocity power distribution;

Figure 8 is a plot of another modulation pattern for use in the lidar system of Figure 1 with the algorithm of Figure 5; Figure 9 shows some more example frequency modulation patterns for use in the lidar system of Figure 1 with the algorithm of Figure 5;

Figure 10 is a schematic view of a phase modulated continuous wave Doppler lidar system;

Figure 1 1 is a flow chart of an analysis algorithm based on a matched filter for use with the lidar system of Figure 10; and

Figure 12 is a collection of illustrations of example phase modulation patterns for use in the lidar system of Figure 10. Detailed Description of the Drawings

Figure 1 shows a lidar system 60 and multiple scatterers 28. The scatterers 28 are located at a distance from the lidar system 60. The scatterers 28 may be atmospheric aerosols, for example water droplets, dust and pollen grains. Lidar 60 emits a substantially collimated beam 26 towards a volume of space surrounding the multiple scatterers. The direction of propagation of the beam 26 defines the line of sight of the lidar. Light is back-scattered by the scatterers 28.

The distance between the lidar and a scatterer is known as the range of the scatterer. Figure 2 illustrates the range, labelled R, of a single scatterer 50. The range is measured along the line of sight of the lidar. Each of the scatterers 28 has a total velocity. Figure 2 illustrates the total velocity vector of the single scatterer 50 which is labelled V_T. The component of total velocity in the direction of propagation of the laser beam 26 is referred to as the line of sight velocity. The line of sight velocity of a single scatterer 50 is labelled V in Figure 2. This is a projection of the total velocity vector V_T on to the line of sight of the lidar.

The lidar system of Figure 1 has an optical module and an electronic module. The optical module has a laser 10, which may include an optical amplifier, for example an Erbium Doped Optical Amplifier. A first optical splitter 12 splits the light from the laser into an optical fibre signal path 14 and an optical fibre reference path 16. The signal path 14 and reference path 16 continue independently and recombine at a second optical splitter 30. On the signal path 14, there is an acousto-optic modulator 18. Light in the signal beam may be frequency shifted by the acousto-optic modulator 18. The acousto-optic modulator 18 shifts signals to higher frequencies, which may have a lower noise level. In addition, the acousto-optic modulator 18 allows the lidar to distinguish between positive and negative ranges.

Connected to the acousto-optic modulator 18 is an optical fibre circulator 20. The optical fibre circulator 20 is connected to a fibre end 22 that can emit and collect light. A collimating optic 24 is positioned such that light exiting the fibre end 22 is directed through free space towards scatterers 28 and back-scattered light from the scatterers 28 is guided into the fibre end 22. Light at the second optical splitter 30 is directed towards a pair of balanced photodiodes 32 and converted into an electrical signal. This signal is sent to the electronic module of the lidar.

The electronic module controls modulation of the laser 10 using a sweep generator 40. The electronic module also captures and analyses back scattered light using signals received from the balanced photodiodes 32 of the optical module at a data acquisition module 34. The data acquisition module 34 is connected to a signal processor 36 and a synchronisation module 38. The synchronisation module 38 is also connected to the sweep generator 40. The synchronisation module 38 sends a signal to both the data acquisition module 34 and the sweep generator 40. The data acquisition module 34 sends information to the signal processor 36 for further processing. Processing of the signal will be described in more detail later.

The lidar also includes a laser frequency monitor 42. The laser frequency monitor 42 measures a value of the frequency of the produced laser light, and sends a signal indicative of this value to the data acquisition module 34. An actual measured frequency of produced laser light can differ from the frequency the laser is set to produce. This difference can have an adverse effect on any subsequent analysis. For example, if the input to an analysis step does not correspond exactly to the frequency of laser produced then an uncertainty is introduced into the analysis. The laser frequency monitor 42 allows an actual measured frequency to be used in the analysis of backscattered light. The laser frequency monitor may consist of any suitable method for measuring laser frequency. For example, it may be an interferometer.

The sweep generator 40 of the electronic module generates a continuous wave frequency modulation pattern by sending a signal to the laser 10 to impose a suitable frequency modulation on continuous wave light. The modulation pattern may be a sinusoidal waveform. The modulated light is transmitted to the first optical splitter 12 where it is split into signal and reference beams. The signal beam passes into the acousto-optic modulator 18 and continues along the signal path 14 to the optical fibre circulator 20. The frequency shifted signal beam passes through the optical circulator 20 and exits through the fibre end 22. Light exiting fibre end 22 is collimated by collimating optic 24 to produce a substantially collimated beam 26 which is directed towards scatterers 28. The scatterers 28 may be atmospheric aerosols including water droplets, dust and pollen grains. Scatterers 28 backscatter a fraction of the light in beam 26. The back scattered light is reflected off the collimating optic 24 towards fibre end 22. The back scattered light then re-enters the fibre end 22 and passes through the fibre optic circulator 20 before continuing along the signal path 14 towards fibre coupler 30.

The reference beam travels from the first fibre coupler 12, along the reference path 16, to the second fibre coupler 30. At fibre coupler 30, the back-scattered light is mixed with the reference beam. The mixed beams are directed onto the balanced photodiodes 32, which convert the difference in power of the two mixed beams to a voltage signal. The voltage signal is sent to the data acquisition module 34, which records digitised voltages and transmits them to the signal processor 36. The synchronisation module 38 provides timing information to the data acquisition module 34 and sweep generator 40. The timing information acts to synchronise their respective digitising and signal generating processes. Sweep generator 40 provides a voltage signal to laser 10 to control the optical frequency of the laser 10 to impose a modulation pattern. The data acquisition module 34 simultaneously records the voltage output of the balanced photo diodes 32. The recorded voltages are then transmitted from the data acquisition module to signal processor 36.

To analyse the data received, a matched filter is used. Matched filtering is a technique that can be used to determine the strength of a known signal, or template, in some data that contains noise. In the present case, the template is the data that would be expected to be recorded with the lidar for a scatterer with range R and velocity V, in the absence of noise. The data containing noise is the signal that is recorded by the lidar. Using a matched filter analysis provides a measurement of the distribution of the back- scattered optical power as a function of scatterer range R and line of sight (LOS) velocity V. The range-velocity map may be used to calculate various quantities of interest such as the LOS wind speed at a given range.

Matched filtering involves multiplying recorded data with a complex conjugated copy of a template and then summing all the elements of the resulting waveform. The amplitude of the result is the matched filter output. This amplitude indicates the strength of the known signal in the data. This amplitude can be represented as the colour of a single pixel in a range-velocity profile with, for example, a darker colour indicating a larger amplitude. The range-velocity profile may then be filled in by repeating the matched filter process for other values of R and V within a range, and again assigning each result to a pixel colour.

Figure 3 is a flow chart showing an overview of a matched filter algorithm for Doppler wind lidar. This is implemented in the signal processor 36. The initial data provided to the algorithm are shown in algorithm inputs 810. These are the frequency modulation waveform pattern 812 measured by the laser frequency monitor 42, for example a sinusoidal waveform, as illustrated, and the detector response signal a(t) 814 recorded by the data acquisition module. The third input to the algorithm is a set of range- velocity pairs of interest 816 represented by {(R^ Vi), (R_2, V₂), ... (R_n, V_n)}. The set of range-velocity pairs of interest define an interval of range and an interval of velocity that are to be examined and plotted.

The algorithm calculation steps are labelled by 820. The first step is labelled as 822. For a first range-velocity pair (R^ Vi) a template detector response b^t) is calculated. The template detector response for a given range-velocity pair (R,V) is a calculation of the expected detector response of a point scatterer, at the given range R with the given velocity V, to a modulated signal beam where the beam is modulated using the frequency modulation waveform pattern 812. The template detector response corresponds to the signal that would be recorded by the detector in the absence of noise. In step 822 the template detector response is calculated for point scatterer at range and velocity Vi . The template detector response is dependent on the frequency modulated waveform pattern 812 that is used to create the signal beam and the properties of the frequency modulated waveform pattern 812. Examples of suitable waveform patterns for this algorithm are shown in Figure 4. The matched filter is calculated as the complex conjugate of the template detector response for the given range-velocity pair. In this case, the matched filter h(t) is calculated from the template response b(t) using the following formula: h(R, V, t) = b^*(R, V, t) (1) where R is range and V is line of sight velocity of a scatterer. The explicit dependence on these variables of the two functions, and on a time parameter t, is shown in Equation (1). The right hand side of Equation (1) is the complex conjugate of the template response denoted by a star.

Step 822 further involves transforming the signal 814 into a projected waveform using the matched filter as calculated above. In more detail, for a signal a(t) a cross correlation is calculated between the matched filter h^t), based on the template response b^t), and a(t). The resulting projected waveform can be considered as a projection of the recorded signal 814 onto the template response for a given range and velocity.

An amplitude, Ai_, is then determined from the sum of all the elements of the projected waveform. This sum can be a continuous integral or can be a discrete sum. For example, an amplitude, A, for a certain range R and line of sight velocity V can be determined using the following equation:

The amplitude is a calculation of the size of the projected waveform. The amplitude of the projected waveform is an indication of the strength of the template signal in the recorded data 814. A high value of amplitude and thus a higher cross-correlation means the detected response is more correlated with the template response than a lower amplitude. The magnitude of the amplitude can then be represented by a shade or colour. For example, a first calculated amplitude that is larger than a second calculated amplitude could be represented by a darker colour than the second amplitude. Step 822 is completed by assigning the shade to a pixel or area on a range-velocity plot 832 that corresponds to the (R^ Vi) point of interest. Step 2 of the algorithm 822 is a repeat of step 1 for a different range-velocity pair of interest (R_2, V₂). A new template detector response b₂(t) is calculated for (R_2, V₂) and a corresponding matched filter h₂(t) based on b₂(t) is also calculated. The detector response a(t) is transformed into a projected waveform by calculating a cross- correlation between the detector response a(t) and matched filter h₂(t). A second amplitude, A_2, is then calculated and represented by a shade or colour on the range- velocity plot 832. As a result of step 2, a second pixel or area on range-velocity plot 832 corresponding to (R_2, V₂) is shaded indicating the strength of the calculated amplitude.

Algorithm 822 continues for every pair in the set of range-velocity pairs of interest {(R^ i), (R_2, V₂), ... (R_n, V_n)}. For a given pair, labelled by the index i, a template response bi(t) is calculated and a corresponding matched filter hi(t). The signal a(t) 814 is then transformed into a projected waveform by calculating a cross-correlation between h,(t) and a(t). A size or amplitude of the projected waveform is then calculated. For every range-velocity pair in this set of range-velocity pairs of interest the range-velocity plot 832 is populated with different shades. After all range-velocity pairs of interest are analysed the resulting algorithm output 830 is a range-velocity plot 832 in which every pixel of interest is shaded.

One of the inputs 812 to the algorithm above is the frequency modulated pattern 812. The accuracy of any calculation of amplitude used to determine the range-velocity plot is dependent on the properties of this pattern 812. A poor choice of pattern can result in a range-velocity plot that is a blurred version of the true distribution of scatterers. For example, a continuous wave transmitted beam without any frequency modulation results in a range-velocity plot that is a blurred version of the true distribution. For this example, the blurring reflects a complete loss of information about the range distribution of scatterers. Suitable frequency modulation waveform patterns for the analysis of Figure 3 can be determined using a mathematical analysis. The extent of blurring caused by a chosen modulation waveform pattern can be quantified by a function known as an ambiguity function. The ambiguity function is a two-dimensional function in the parameters range and velocity. A range-velocity profile constructed from data is a mathematical convolution of the ambiguity function and the true distribution of scatterers. Mathematically, the ambiguity function x(R, V) is calculated using the following integral:

where g(t) is a function representing the transmitted beam in complex baseband representation, R is the range of a scatterer, V is the LOS velocity of the scatterer, t is a time parameter, v is optical frequency of the laser and c is the speed of light.

As can be seen from Equation (3) the ambiguity function is completely determined by choice of the form of transmitted waveform g(t) and thus by a choice of underlying modulation pattern. An ambiguity function that has an infinite peak at R=0 and V=0, and a value of zero at other values of R and V would provide a range-velocity profile with no blurring. However, in practice an infinite peak is not possible and the ambiguity function must have a central peak of a non-zero finite width. A suitable form of the ambiguity function for this analysis is a function with a single peak centred at R=0 and V=0 with a low value for all other values of R and V. Such a suitable ambiguity function will result in a range-velocity map that provides an approximation to the true distribution of scatterers in terms of range and LOS velocity.

Given that the desired form of the ambiguity function is known, the suitable transmitted waveform that can provide the desired ambiguity function should be determined. Equation (3) shows the relationship between the waveform and the ambiguity function. The ambiguity function is neither injective nor surjective. In other words, not every possible ambiguity function has a waveform that will produce it and some ambiguity functions can be produced by more than one waveform. Therefore, whilst it is straight- forward to determine the ambiguity function from the transmitted waveform by using Equation (3), no corresponding equation exists that would calculate which, if any, transmitted waveform would provide a certain ambiguity function.

As noted above, a suitable frequency modulated waveform is a sinusoidal frequency modulated waveform. This provides an ambiguity function that has a value only in a small region around a point in the range-velocity parameter space and low values elsewhere in this space. The modulated signal is represented mathematically as follows: g(t) = K exp sin(27rat) (4) where g(t) represents the transmitted waveform in complex baseband representation, K is the transmitted waveform amplitude, L is the peak-mean frequency modulation amplitude, a is the modulation frequency of the waveform and t is a time parameter. This signal is transmitted and the predicted template signal from a single scatterer for this value of range R and line of sight velocity V is: b(R, V; t) = K exp Vt (5)

Other parameters appearing in equation (5) are the optical frequency of the laser v and the speed of light c. A matched filter is calculated from this predicted signal form as set out in Equation (1) as follows: h(R, V; t) = K^* exp Vt (6)

Following step 822 the recorded signal a(t) is transformed into a projected waveform, using the above matched filter, and a measurement of the size of the projected waveform is calculated. This is calculated as follows:

A(R, V = Vt dt (7)

Figure 4 shows various modulation waveform patterns that can be used with the analysis method of Figure 3. In all the examples shown in Figure 4 laser frequency is plotted on the vertical axis and time is plotted on the horizontal axis. The waveform pattern will be repeated to form the waveform for use in the continuous wave lidar. In all of Figures 4(a) to (e) and (g) to (i), the waveform has more than two different slopes.

In general, a suitable waveform for the analysis method of Figure 3 is one that provides a desired ambiguity function as described above. In particular, it is found that a waveform containing more than two different slopes is a suitable waveform. The pattern of Figure 4(a) is a series of multiple linear slopes consisting of up-sweep and down-sweep pairs. The maximum and minimum laser frequency of each up-sweep and down-sweep is a constant value. The gradient increases for each subsequent upsweep. In other words, the waveform reaches the maximum value in less time for each subsequent up-sweep. Each up-sweep has a corresponding down-sweep with a negative gradient of the same magnitude as the up-sweep. The waveform of Figure 4(a) shows eleven different slopes (including the first, flat, part of the waveform as one slope). Figure 4(b) shows a single period of a sinusoidal function. At each point on the sinusoidal waveform a tangent line can be drawn that corresponds to the slope of the waveform. Advantageously a sinusoidal pattern is easy to create in practice. Figure 4(c) shows a phase shifted sinusoidal function, in this case, a cosine function. Figure 4(d) shows a sinusoidal waveform pattern having more than one period.

Figure 4(e) shows an irregular waveform that has multiple different gradients. Figure 4(f) shows a more regular, symmetric waveform, in this case a triangular waveform. This has a regular series of up and down sweep pairs. Each down sweep has an equal in magnitude gradient to its corresponding up sweep partner but the gradient is in the opposite direction. The repeating waveform of Figure 4(f) has only two different slopes. In general, a small number of different gradients will result in a blurry image reconstruction, and so this is not ideal.

Figure 4(g) is a variation of the waveform of Figure 4(a) in which each saw tooth is defined by curves. Figure 4(h) shows a variation of the waveform of Figure 4(c) in which the waveform has a series of small steps. Although a smooth waveform is preferred, Figure 4(h) is an approximation of a smooth waveform pattern. Each step of the waveform of Figure 4(h) has a different slope. Figure 4(i) shows a waveform with a smaller total frequency variation compared to Figure 4(c). In general, a larger total frequency variation corresponds to a better range resolution. Therefore, if better range resolution is desired then Figure 4(c) is preferred to Figure 4(i).

Figure 5 is a flow chart showing an overview of another matched filter based analysis method that can be performed by the signal processor 36. This process uses a frequency modulation that has a plurality of linear slopes, preferably more than two different linear slopes. Initial data 1 10 provided to the algorithm are the modulation pattern 120 generated by the sweep generator 40, and a response signal 122 recorded by the data acquisition module 34. The modulation pattern 120 is represented by a plot. The vertical axis of the plot indicates optical frequency, labelled by v, and the horizontal axis indicates time, labelled by t. An important property of the modulation pattern 120 is the rate of change of optical frequency with respect to time. This is a mathematical definition of the slope of the modulation pattern at a given point in the modulation pattern 120. The modulation pattern 120 consists of multiple sloping segments. In the example shown in Figure 5, the set of segments make up a series of linear sweeps in the form of a triangular type waveform such that each up-sweep segment is followed by a subsequent down-sweep segment. Figure 5 shows that the slope of the up-sweep segment is equal and opposite to the slope of the subsequent down-sweep segment. In the example shown in Figure 5, the slope of each up-sweep segment is less for each subsequent up-sweep in the series of up-sweep segments, while the maximum value of the up-sweep is constant. In other words, the rate of change of frequency is decreasing with each subsequent up-sweep in the modulation pattern 120. The measured response signal 122 is dependent on back-scattered light. The response signal 122 is split into distinct sections that correspond to the modulation pattern 120. In the example shown in Figure 6, step 1 12 shows how the response signal 122 is divided into portions 126 where each individual portion 126 corresponds to an individual segment of the modulation pattern 120. Each portion 126 consists of data recorded whilst a single linear sweep is being generated. In the absence of noise, the expected response signal from each scatterer for each linear segment of the input signal would be a sinusoid. As can be seen, however, each portion 126 of the response signal appears noisy. Each signal portion 126 is transformed 114 using a Fourier transform into a projected waveform. A fourier transform uses sinusoids to pick out different signal frequencies. Since the expected signal response from each scatterer for each linear section of the input signal is a sinusoid, this means that the fourier transform effectively performs a matched filter analysis on each signal portion. The projected waveform is a frequency spectrum 128 for each of the signal portions 126. A Fourier transform of a signal in the time domain, a(t), is a projection of the signal a(t) onto a basis set of functions e^2mft at a given time and summed over all times to produce a projected waveform A(f). Mathematically, the Fourier transform A(f) of the signal a(t), from the time to the frequency domain, can be written as:

This is a continuous Fourier transform using an integral over time. Alternatively, the Fourier transform can be calculated as a discrete sum over time. The integral or sum is taken over the time duration of the signal portion 126.

Advantageously, transformation 1 14 of the signal is performed using the computationally efficient Fast Fourier Transform algorithm. The result is a collection of frequency spectra 128 where each frequency spectrum 128 corresponds to a sloping segment of the underlying modulation pattern 120. The frequency spectra 128 are representations of the amplitude of parts of the response signal 122 in a frequency space.

Step 1 16 is a mapping of the frequency spectra 128 to a corresponding range-velocity profile 130. Step 1 16 of Figure 5 shows the calculation of back-projection of the frequency spectra 128. It can be considered a smearing of the frequency spectrum 128 in the range-velocity plane in an angular direction. The angular direction of smearing corresponds to the magnitude of the slope of the corresponding segment of the modulation pattern 120. In the example shown in Figure 5, three range-velocity profiles 130 are shown for illustrative purposes. The first range-velocity profile corresponds to the first up-sweep of the modulation pattern 120. The second range- velocity profile corresponds to the first down-sweep of the modulation pattern 120. The third range-velocity profile pictured corresponds to the final down-sweep of the modulation pattern 130. Figure 6 shows a more detailed example of this calculation.

Figure 6 illustrates a mapping between a measured signal spectrum and a range- velocity power profile for a single scatterer. Plot 70 shows an amplitude frequency spectrum A(f). The frequency spectrum is centred about a single peak 78 centred at a signal frequency f₀. The peak 78 has a width Af. Plot 72 is an example of a range- velocity power profile. The vertical axis of plot 72 indicates scatterer range R. The horizontal axis of plot 72 indicates scatterer velocity V. Plot 72 shows a line 76 with a positive gradient intercepting the horizontal axis. On either side of the line 76 are two parallel lines defining a shaded band 74. The mapping illustrated in Figure 6 is based on the following equation:

Equation (9) is a well-known relationship between the measured signal frequency f, the range of the scatterer R , and the line of sight velocity of the scatterer V. Equation (9) is also dependent on the speed of the light, c, the laser optical frequency, v, and the rate of change of laser optical frequency or sweep speed, dv/dt. The sweep speed is graphically represented as the slope of the modulation pattern. This equation contains only two unknown terms, which are R and V (all other terms are known or measured independently). Equation (9) is a mathematical description of a linear relationship between R and V that forms the basis of a mapping between amplitude frequency spectrum 70 and range-velocity profile 72. Substituting f = f₀ into equation (9) results in a linear relationship between R and V as described by line 76 in plot 72. Shaded band 74 corresponds to all possible combinations of R and V that contribute to peak 78. Sweep speed dv/dt determines the gradient of the line 76 in the range-velocity profile 72.

When multiple scatterers are present, any scatterer at a range R and with line of sight velocity V outside of the values of the shaded band 76 show up as peaks at other frequencies in the spectrum A(f) . Therefore, a spectrum obtained as a result of a single linear frequency modulation continuous wave sweep can be considered as a cross sectional view through a range-velocity power distribution, where the angle of this cross section is determined by the sweep speed dv/dt. A measured signal spectrum 78 may be used to compute a back-projection of this spectrum. A back-projection consists of the spectrum 78 smeared along the R-V plane in a direction defined by the line 76.

Returning to Figure 5, it is shown that each of the range-velocity profiles 130 is made up of multiple parallel shaded bands. The angle of the multiple shaded bands is dependent on the slope of the corresponding linear sweep. The colour of each band corresponds to the values of the frequency spectrum. Once these are determined for each segment of the modulated light, step 1 18 involves creating a power density profile 132 using the one or more range-velocity profiles 130. The power density profile 132 is the result of a summing together of the back-projections. The resulting power density profile 132 is shown in more detail in Figure 7.

The algorithm of Figure 5 is a specialised version of the algorithm of Figure 3. If the same frequency modulation waveforms are provided to input 812 of Figure 3 and input 120 of Figure 5; and the same data is provided to input 814 of Figure 3 and input 122 of Figure 5, then the output 832 of Figure 3 will be the same as the output 132 of Figure 5. In the output 132 of the algorithm of Figure 5, each pixel is calculated with an implementation of a matched filter algorithm. An important difference between the algorithms of Figure 3 and Figure 5 is that for Figure 3, each pixel is calculated explicitly using a matched filter algorithm, whereas in Figure 5, the values for each pixel are calculated in parallel and only when the entire algorithm is complete is the final value of each pixel known.

Figure 7 is a plot of a range-velocity power distribution. The horizontal axis of the plot indicates line of sight velocity, V. The vertical axis indicates scatterer range, R. The plot is a shaded map. Lighter shades indicate a lower value of back-scattered power density and darker shades indicate a higher value of back-scattered power density. The lidar does not determine the range R and line of sight velocity V of individual scatterers as it has a finite resolution which is greater than the typical scatterer spacing, described by the ambiguity function. Well known methods can be used to extract useful information from the range - velocity power distribution. For example, the location of the peak value along a line of constant R can be used to measure the line of sight wind velocity at that range. Additionally, the width of the peak along the velocity axis can be used to provide a measure of the amount of air turbulence. Figure 8 shows another example of a frequency modulation pattern that could be used for the analysis of Figure 5. In particular, Figure 8(a) shows a substantially equally distributed slopes frequency modulation pattern. The modulation pattern has multiple sloping segments each with a different gradient. Each segment has a linear slope. For ease of illustration, a limited number of linear slope sections are shown in Figure 8(a). The laser frequency is indicated on the vertical axis and time t is indicated on the horizontal axis.

Figure 8(a) shows a series of up-sweep and down-sweep pairs forming a triangular waveform. Each up-sweep segment has a larger maximum value than the previous upsweep segment. Each up-sweep segment is of the same time duration. In this way, the magnitude of the slope of each subsequent up-sweep is greater than the magnitude pf the preceding up-sweep. This is shown explicitly in Figure 8(b), which shows the slope or derivative of the frequency of the segments of the modulation pattern of Figure 8(a). From Figure 8(b), it can be seen the magnitudes of the slopes of the modulation pattern increase in time. Each value of slope for an up-sweep segment is followed by an equal in magnitude and opposite in sign slope for the following down-sweep segment. Figure 8(c) is a histogram of slopes shown in Figure 8(b) and generated by the modulation pattern of Figure 8(a). The frequency modulation pattern is repeated in time to produce an even distribution of slopes with respect to the magnitude of slopes. Figure 8(c) shows a series of bins, each bin corresponding to a different value of the derivative of the slope segment. A count of the values of the derivative of the slopes is completed. Figure 8(c) shows a substantially even distribution of slopes. Therefore, the modulation pattern shown in Figure 8(a) can be considered to be a substantially evenly distributed slope modulation pattern. Advantageously, a larger number of linear slope sections would be used for a measurement, as this creates a more even distribution of slopes.

Figure 9 shows further examples of frequency modulation waveforms that are suitable for the analysis method of Figure 5. In all the examples shown in Figure 9 laser frequency is plotted on the vertical axis and time is plotted on the horizontal axis. The waveform pattern is repeated in time to generate continuous wave lidar. In general, a waveform pattern suitable for the analysis method of Figure 5 contains multiple linear slopes with different gradients. All the patterns of Figure 9 contain more than two different linear slopes.

Figure 9(a) shows a waveform that has a series of multiple linear slopes consisting of a series of up-sweep and down-sweep pairs. The maximum and minimum laser frequency of each up-sweep and down-sweep is a constant value. The gradient increases for each subsequent up-sweep. In other words, the waveform reaches the maximum value in less time for each subsequent up-sweep. Each up-sweep has a corresponding down-sweep with a negative gradient of the same magnitude as the up- sweep.

In general, the order of the slopes is not important. Irregular patterns can generate suitable waveforms. Figure 9(b) shows a waveform made up from a series of up and down slope pairs. In contrast to Figure 9(a), in this case the up-sweep has a positive gradient of a first magnitude and the subsequent down-sweep has a negative gradient of a second magnitude where the second magnitude does not equal the first magnitude. Figure 9(c) shows a waveform with discontinuities. As certain lasers can take time to alter their frequency, it may be preferable to avoid discontinuities. A waveform formed to maximise the time duration of each linear slope will lead to improved resolution. Figure 9(d) is an example of how this can be achieved. The waveform of Figure 9(d) has a series of up and down-sweep pairs where each down- sweep has the same magnitude of gradient as its corresponding up-sweep partner. In contrast to Figure 9(a), each slope increases or decreases for the same length of time. The magnitude of the gradient of each pair increases with each subsequent pair. As the magnitude of the gradient increases during the same length of time, the maximum value of each up and down sweep pair also increases with each subsequent pair. The final pair in Figure 9(d) has a maximum value equal to the maximum frequency of the laser. The waveform pattern is constrained by time available. The dotted line in Figure 9(d) shows an example continuation of the first slope. If more time is available an improved resolution can be achieved by increasing each up-sweep slope as long as possible. In such a case, the up-sweep could be limited by the maximum and minimum frequency that the laser is capable of producing. Figure 9(e) shows a pattern where the down-sweep segment does not return to the minimum laser frequency. Figure 9(f) shows a pattern where the first up-sweep segment is split into two up-sweep sub-segments of the same gradient. The pattern increases for the first up-sweep segment and then plateaus for a period of time before continuing to increase in the second up-sweep sub-segment. While a waveform generated from such a pattern is suitable, it is preferable to avoid multiple sub- segments as the analysis of Figure 5 processes each sub-segment separately.

Figure 9(g) shows a waveform where the first up-sweep is made up of small steps. The first up-sweep approximates a smooth slope. The waveform could be composed of steps to approximate a smooth slope. A smooth waveform is preferred over a stepped waveform. Figure 9(h) shows a waveform having sloping segments that are approximately linear. While a pattern with non-linear slopes can be used, the analysis of Figure 5 produces a higher quality of reconstructed image when a linear pattern is used. The quality of the reconstructed image produced by this analysis method will improve the closer to linear the slopes are. Figure 9(i) shows a waveform that has a non-linear part in amongst a series of linear up and down sweeps. The non-linear parts of a waveform will be left out of the data processing step of the analysis of Figure 5. It is preferred that the total duration of such extraneous non-linear parts are minimised in the waveform.

In general, the resolution of the reconstructed image produced by the analysis method of Figure 5 will improve with increased number of sloping segments with different gradients. Figure 9(j) shows an example of a waveform pattern that would lead to a reconstructed image of lower quality than the waveform of Figure 9(a). Figure 9(j) shows a waveform pattern with only two up-sweep and down-sweep pairs. In contrast to Figure 9(a) the waveform pattern of Figure 9(j) only has two gradient magnitudes.

The lidar system 60 described above relies upon frequency modulation of the laser 10. This may be achieved in a number of different ways. For example, an optical path length of a resonant cavity of the laser 10 may be modulated. Alternatively, the laser 10 may be a single frequency laser and the frequency of the light emitted by the laser 10 may be modulated after the light has been emitted by the laser 10. For example, the lidar system 60 may include a frequency modulator located anywhere along the optical path between the laser 10 and the first optical splitter 12. Alternatively, the lidar system 60 may include a frequency modulator located anywhere along the signal path 14 between the first optical splitter 12 and the scatterers 28.

Figure 10 shows an alternative lidar system 260 and multiple scatterers 228. The scatterers 228 are located at a distance from the lidar system 260. The scatterers 228 may be atmospheric aerosols, for example water droplets, dust and pollen grains. Lidar 260 emits a substantially collimated beam 226 towards a volume of space surrounding the multiple scatterers. The direction of propagation of the beam 226 defines the line of sight of the lidar. Light is back-scattered by the scatterers 228.

The lidar system 260 of Figure 10 has an optical module and an electronic module. The optical module has a laser 210 for generating a fixed optical frequency. The laser 210 may include an optical amplifier, for example an Erbium Doped Optical Amplifier. A first optical splitter 212 splits the light from the laser 210 into an optical fibre signal path 214 and an optical fibre reference path 216. The signal path 214 and reference path 216 continue independently and recombine at a second optical splitter 230. On the signal path 214, there is an acousto-optic modulator 218, a phase modulator 217 and, optionally, an optical amplifier 219. Light in the signal beam may be frequency shifted by the acousto-optic modulator 218. The acousto-optic modulator 218 shifts signals to higher frequencies, which may have a lower noise level. In addition, the acousto-optic modulator 218 allows the lidar to distinguish between positive and negative ranges.

If the optical amplifier 219 is present, the optical amplifier 219 is connected to an optical fibre circulator 220. If the optical amplifier 219 is absent, the phase modulator 217 is connected to the optical fibre circulator 220. The optical fibre circulator 220 is connected to a fibre end 222 that can emit and collect light. A collimating optic 224 is positioned such that light exiting the fibre end 222 is directed through free space towards scatterers 228 and back-scattered light from the scatterers 228 is guided into the fibre end 222. Light at the second optical splitter 230 is directed towards a pair of balanced photodiodes 232 and converted into an electrical signal. This signal is sent to the electronic module of the lidar.

The electronic module controls modulation of the phase modulator 217 using a waveform generator 240. The electronic module also captures and analyses back scattered light using signals received from the balanced photodiodes 232 of the optical module at a data acquisition module 234. The data acquisition module 234 is connected to a signal processor 236 and a synchronisation module 238. The synchronisation module 238 is also connected to the waveform generator 240. The synchronisation module 238 sends a signal to both the data acquisition module 234 and the waveform generator 240. The data acquisition module 234 sends information to the signal processor 236 for further processing. Processing of the signal will be described in more detail later.

The waveform generator 240 of the electronic module generates a phase modulation pattern by sending a signal to the phase modulator 217 to impose a suitable phase modulation on continuous wave light. The modulation pattern may be a binary coded phase modulation waveform. If the optical amplifier 219 is present the phase modulated light is transmitted to the optical amplifier 219 which amplifies the light and transmits the amplified light to fibre optic circulator 220. If the optical amplifier is absent the phase modulated light is transmitted to fibre optic circulator 220. The phase modulated signal beam passes through the optical circulator 220 and exits through the fibre end 222. Light exiting fibre end 222 is collimated by collimating optic 224 to produce a substantially collimated beam 226 which is directed towards scatterers 228. The scatterers 228 may be atmospheric aerosols including water droplets, dust and pollen grains. Scatterers 228 backscatter a fraction of the light in beam 226. The back scattered light is reflected off the collimating optic 224 towards fibre end 222. The back scattered light then re-enters the fibre end 222 and passes through the fibre optic circulator 220 before continuing along the signal path 214 towards fibre coupler 230. The reference beam travels from the first fibre coupler 212, along the reference path 216, to the second fibre coupler 230. At fibre coupler 230, the back-scattered light is mixed with the reference beam. The mixed beams are directed onto the balanced photodiodes 232, which convert the difference in power of the two mixed beams to a voltage signal. The voltage signal is sent to the data acquisition module 234, which records digitised voltages and transmits them to the signal processor 236. The synchronisation module 238 provides timing information to the data acquisition module 234 and waveform generator 240. The timing information acts to synchronise their respective digitising and signal generating processes. Waveform generator 240 provides a voltage signal to the phase modulator 217 to control the optical phase of light in the signal path 214 before the light reaches the scatterers 228 to impose a phase modulation pattern. The data acquisition module 234 simultaneously records the voltage output of the balanced photo diodes 232. The recorded voltages are then transmitted from the data acquisition module to signal processor 236. To analyse the data received, a matched filter is used in a similar way to that already described for frequency modulation with reference to the lidar system 60 of Figure 1.

Figure 1 1 is a flow chart showing an overview of a matched filter algorithm for Doppler wind lidar for use with the lidar system 260 of Figure 10. This is implemented in the signal processor 236. The initial data provided to the algorithm are shown in algorithm inputs 910. These are the phase modulation waveform pattern 912, for example a binary coded waveform φ(ί), as illustrated, and the detector response signal a(t) 914 recorded by the data acquisition module. The third input to the algorithm is a set of range-velocity pairs of interest 916 represented by {(R^ Vi), (R_2, V₂), ... (R_n, V_n)}. The set of range-velocity pairs of interest define an interval of range and an interval of velocity that are to be examined and plotted.

The algorithm calculation steps are labelled by 920. The first step is labelled as 922. For a first range-velocity pair (R^ Vi) a template detector response b^t) is calculated. The template detector response for a given range-velocity pair (R,V) is a calculation of the expected detector response of a point scatterer, at the given range R with the given velocity V, to a modulated signal beam where the beam is modulated using the frequency modulation waveform pattern 912. The template detector response corresponds to the signal that would be recorded by the detector in the absence of noise. In step 922 the template detector response is calculated for point scatterer at range and velocity Vi_. The template detector response is dependent on the phase modulated waveform pattern 912 that is used to create the signal beam and the properties of the phase modulated waveform pattern 912. Examples of suitable waveform patterns for this algorithm are shown in Figure 12.

The matched filter is calculated as the complex conjugate of the template detector response for the given range-velocity pair. In this case, the matched filter h(t) is calculated from the template response b(t) using Equation (1).

Step 922 further involves transforming the signal 914 into a projected waveform using the matched filter as calculated above. In more detail, for a signal a(t) a cross correlation is calculated between the matched filter h^t), based on the template response b^t), and a(t). The resulting projected waveform can be considered as a projection of the recorded signal 914 onto the template response for a given range and velocity.

An amplitude, Ai_, is then determined from the sum of all the elements of the projected waveform. This sum can be a continuous integral or can be a discrete sum. For example, an amplitude, A, for a certain range R and line of sight velocity V can be determined using Equation (2).

The amplitude is a calculation of the size of the projected waveform. The amplitude of the projected waveform is an indication of the strength of the template signal in the recorded data 914. A high value of amplitude and thus a higher cross-correlation means the detected response is more correlated with the template response than a lower amplitude. The magnitude of the amplitude can then be represented by a shade or colour. For example, a first calculated amplitude that is larger than a second calculated amplitude could be represented by a darker colour than the second amplitude. Step 922 is completed by assigning the shade to a pixel or area on a range-velocity plot 932 that corresponds to the (R^ Vi) point of interest.

Step 2 of the algorithm 922 is a repeat of step 1 for a different range-velocity pair of interest (R_2, V₂). A new template detector response b₂(t) is calculated for (R_2, V₂) and a corresponding matched filter h₂(t) based on b₂(t) is also calculated. The detector response a(t) is transformed into a projected waveform by calculating a cross- correlation between the detector response a(t) and matched filter h₂(t). A second amplitude, A_2, is then calculated and represented by a shade or colour on the range- velocity plot 932. As a result of step 2, a second pixel or area on range-velocity plot 932 corresponding to (R_2, V₂) is shaded indicating the strength of the calculated amplitude.

Algorithm 922 continues for every pair in the set of range-velocity pairs of interest {(R^ \ ), (R_2, V₂), ... (R_n, V_n)}. For a given pair, labelled by the index i, a template response bi(t) is calculated and a corresponding matched filter hi(t). The signal a(t) 914 is then transformed into a projected waveform by calculating a cross-correlation between h,(t) and a(t). A size or amplitude of the projected waveform is then calculated. For every range-velocity pair in this set of range-velocity pairs of interest the range-velocity plot 932 is populated with different shades. After all range-velocity pairs of interest are analysed the resulting algorithm output 930 is a range-velocity plot 932 in which every pixel of interest is shaded.

One of the inputs 912 to the algorithm above is the phase modulated pattern 912. The accuracy of any calculation of amplitude used to determine the range-velocity plot is dependent on the properties of this pattern 912. A poor choice of pattern can result in a range-velocity plot that is a blurred version of the true distribution of scatterers. For example, a continuous wave transmitted beam without any phase modulation results in a range-velocity plot that is a blurred version of the true distribution. For this example, the blurring reflects a complete loss of information about the range distribution of scatterers.

Suitable phase modulation waveform patterns for the analysis of Figure 1 1 can be determined using a mathematical analysis similar to that used to determine the frequency modulation waveform patterns for the analysis of Figure 3.

As noted above, a suitable phase modulated waveform is a binary code phase modulated waveform. Figure 12 shows various phase modulation waveform patterns that can be used with the analysis method of Figure 1 1. In all the examples shown in Figure 12 optical phase is plotted on the vertical axis and time is plotted on the horizontal axis. The waveform pattern will be repeated to form the waveform for use in the continuous wave lidar. In all of Figures 12(a) to (c), the waveform has at least two different discrete phase values. In general, a suitable waveform for the analysis method of Figure 12 is one that provides a desired ambiguity function as described above. In particular, it is found that a waveform containing two or more different discrete phase values is a suitable phase modulation waveform. For example, the phase modulation patterns of Figure 12(a) and 12(b) each comprise a binary coded phase modulation waveform which varies between two binary values which are 180 degrees apart. A binary coded phase modulation may be relatively easy to implement. The binary coded phase modulation waveform of Figure 12(a) comprises a pseudo-random binary sequence. The binary coded phase modulation waveform of Figure 12(b) comprises a binary Barker code. A binary Barker code has the advantage of low side-lobe level, meaning that the range- velocity map produced when using such a code will have good contrast. There are seven known Barker Codes, one of which is shown by way of example in Figure 12(b).

Figure 12(c) shows another suitable phase modulation waveform which comprises a polyphase coded modulation waveform which varies between more than two discrete values. The implementation of a polyphase coded modulation waveform requires slightly more complex hardware than a binary coded modulation waveform because a polyphase coded modulation waveform is an analogue signal that can take multiple values rather than a binary, digital signal. However, the use of a polyphase coded modulation waveform gives more flexibility in waveform choice, allowing improvements in the resolution and contrast of the range-velocity map. An example class of polyphase coded modulation waveforms that can be used are the polyphase Barker Coded waveforms. These are the polyphase coded waveform analogue of the binary Barker Coded waveforms, and they have the advantage of low sidelobe level leading to good contrast in the range velocity map.

The lidar system 260 described above with reference to Figure 10 relies upon the use of phase modulation of the light emitted from a fixed frequency laser 210 at a position in the signal path 214 between the acousto-optic modulator 218 and the circulator 220. However, one of ordinary skill in the art should understand that the phase of the light may be modulated at a position anywhere in the signal path 214 between the first optical splitter 212 and the scatterers 228. Alternatively, the lidar system 260 may include a phase modulator located between the laser 210 and the first optical splitter 212.

One of skill in the art will understand that it may be possible to use a combination of phase modulated and frequency modulated continuous wave light to provide a range- velocity plot for the scatterers 28, 228. Whilst the lidar systems 60, 260 described above use fibre based optics, these can be replaced by free space optics and vice versa. Also, additional hardware may be used in the lidar system 60 to monitor the frequency of the laser 10 during the measurement. Any discrepancy between actual laser frequency and intended laser frequency can, if large enough, can cause distortion to or error in the measurement result. The monitoring hardware may take the form of an interferometer. Alternative components may be used in the lidar systems 60, 260. For example, the collimators 24, 224 are depicted as being reflective. There are many well-known ways of collimating a laser beam which may be used in place of collimators 24, 224 including reflective, refractive and diffractive means, or combinations of these. In addition, the fibre optic circulators 20, 220 may be replaced with an alternative that has a higher attenuation of the unwanted light path directly between acousto-optic modulators 18, 218 and fibre splitters 30, 230. This will reduce the amplitude of the largest unwanted signal component and reduce the required dynamic range of the balanced photodiodes 32, 232. The alternative may consist of a free space optics, polarisation based circulator design consisting of a wedged polarising beam splitting plate followed by a half wave plate.

A skilled person will appreciate that variations of the enclosed arrangement are possible without departing from the invention. For example, alternative image reconstruction algorithms may also be implemented. Accordingly, the above description of the specific embodiment is made by way of example only and not for the purposes of limitations. It will be clear to the skilled person that minor modifications may be made without significant changes to the operation described.

Claims

A method for determining range and velocity information for a collection of moving scatterers comprising:

transmitting the modulated signal beam to the collection of scatterers; detecting light back-scattered by the collection of scatterers, and analysing the detected signal using a matched filter to provide range and velocity information for the collection of scatterers.

A method as claimed in claim 1 comprising frequency modulating continuous wave light so that the modulated signal beam comprises a frequency modulated signal beam.

A method as claimed in claim 2 wherein the frequency modulated signal beam comprises more than two slopes.

A method as claimed in claim 2 or 3 wherein the frequency modulated signal beam comprises multiple linear sections.

A method as claimed in claim 4 wherein the frequency modulated signal beam comprises multiple linear sections each with a different gradient.

A method as claimed in claim 4 or 5 wherein the frequency modulated signal beam comprises at least three linear sections each with a different gradient.

A method as claimed in any one of claims 4 to 6 wherein analysing the detected signal using a matched filter involves analysing the detected signal

corresponding to each linear section using a Fourier transform.

8. A method as claimed in any one of claims 2 to 7, wherein the frequency

modulated signal beam comprises a triangular waveform.

9. A method as claimed in claim 8 wherein the frequency modulated signal beam comprises multiple triangular waveforms.

10. A method as claimed in claim 9 wherein each triangle has the same duration but a different height.

1 1. A method as claimed in claim 10 wherein the height increases as a function of time.

12. A method as claimed in claim 10 wherein the height decreases as a function of time.

13. A method as claimed in claim 9 wherein each triangle is of the same height but a different duration.

14. A method as claimed in claim 13 wherein the duration increases as a function of time.

15. A method as claimed in claim 13 wherein the duration decreases as a function of time.

16. A method as claimed in claim 2 or 3 wherein the frequency modulated signal beam comprises a sinusoidal waveform.

17. A method as claimed in any one of claims 2 to 16 comprising using a reference beam that is substantially the same as the frequency modulated signal beam.

18. A method as claimed in any one of claims 2 to 17 comprising monitoring the frequency of the frequency modulated signal beam and using the monitored frequency in the matched filter analysis.

19. A method as claimed in any preceding claim comprising phase modulating

continuous wave light so that the modulated signal beam comprises a phase modulated signal beam.

20. A method as claimed in claim 19 wherein the phase modulated signal beam comprises a binary coded phase modulation waveform which varies between two binary values.

21. A method as claimed in claim 20 wherein the two binary values differ by 180 degrees.

22. A method as claimed in claim 20 or 21 wherein the binary coded phase

modulation waveform comprises a pseudo-random binary sequence.

23. A method as claimed in claim 20 or 21 wherein the binary coded phase

modulation waveform comprises a binary Barker code.

24. A method as claimed in claim 19 wherein the phase modulated signal beam comprises a polyphase coded modulation waveform which varies between more than two discrete values.

25. A method as claimed in claim 24 wherein the polyphase coded modulation waveform comprises a polyphase Barker code.

26. A method as claimed in any preceding claim wherein the modulated signal beam comprises a substantially collimated beam of light.

27. A method as claimed in any of the preceding claims wherein the range and velocity information comprises a range-velocity profile or map.

28. A method as claimed in any of the preceding claims wherein the scatterers comprise atmospheric aerosols.

29. A method as claimed in any of the preceding claims comprising using the range and velocity information for the collection of scatterers to provide a measure of wind speed.

30. A method as claimed in any of the preceding claims comprising using the range and velocity information for the collection of scatterers to provide a measure of air turbulence.

31. A system for determining range and velocity information for a collection of moving scatterers, the system being configured to:

transmit the modulated signal beam to the collection of scatterers; detect light back-scattered by the collection of scatterers, and analyse the detected signal using a matched filter to provide range and velocity information for the collection of scatterers.

32. A system as claimed in claim 31 wherein the system is configured to frequency modulate continuous wave light so that the modulated signal beam comprises a frequency modulated signal beam.

33. A system as claimed in claim 32 wherein the frequency modulated signal beam comprises more than two slopes.

34. A system as claimed in claim 32 or 33 wherein the frequency modulated signal beam comprises multiple linear sections.

35. A system as claimed in claim 34 wherein the frequency modulated signal beam comprises multiple linear sections each with a different gradient.

36. A system as claimed in claim 34 or 35 wherein the frequency modulated signal beam comprises at least three linear sections each with a different gradient.

37. A system as claimed in any one of claims 34 to 36 wherein analysing the

detected signal using a matched filter involves analysing the detected signal corresponding to each linear section using a Fourier transform.

38. A system as claimed in any one of claims 32 to 37, wherein the frequency modulated signal beam comprises a triangular waveform.

39. A system as claimed in claim 38 wherein the frequency modulated signal beam comprises multiple triangular waveforms.

40. A system as claimed in claim 39 wherein each triangle has the same duration but a different height.

41. A system as claimed in claim 40 wherein the height increases as a function of time.

42. A system as claimed in claim 40 wherein the height decreases as a function of time.

43. A system as claimed in claim 39 wherein each triangle is of the same height but a different duration.

44. A system as claimed in claim 43 wherein the duration increases as a function of time.

45. A system as claimed in claim 43 wherein the duration decreases as a function of time.

46. A system as claimed in claim 32 or 33 wherein the frequency modulated signal beam comprises a sinusoidal waveform.

47. A system as claimed in any one of claims 32 to 46 adapted to use a reference beam that is substantially the same as the frequency modulated signal beam.

48. A system as claimed in any one of claims 32 to 47 adapted to monitor the

frequency of the signal beam and use the monitored frequency in the matched filter analysis.

49. A system as claimed in any one of claims 31 to 48 wherein the system is

configured to phase modulate continuous wave light so that the modulated signal beam comprises a phase modulated signal beam.

50. A system as claimed in claim 49 wherein the phase modulated signal beam comprises a binary coded phase modulation waveform which varies between two binary values.

51. A system as claimed in claim 50 wherein the two binary values differ by 180 degrees.

52. A system as claimed in claim 50 or 51 wherein the binary coded phase

modulation waveform comprises a pseudo-random binary sequence.

53. A system as claimed in claim 50 or 51 wherein the binary coded phase

modulation waveform comprises a binary Barker code.

54. A system as claimed in claim 49 wherein the phase modulated signal beam comprises a polyphase coded modulation waveform which varies between more than two discrete values.

55. A system as claimed in claim 54 wherein the polyphase coded modulation waveform comprises a polyphase Barker code.

56. A system as claimed in any one of claims 31 to 55 comprising a collimator for collimating the modulated signal beam.

57. A system as claimed in any one of claims 31 to 56 wherein the range and velocity information comprises a range-velocity profile or map.

58. A system as claimed in any one of claims 31 to 57 wherein the scatterers comprise atmospheric aerosols.

59. A system as claimed in any one of claims 31 to 58 adapted to use the range and velocity information for the collection of scatterers to provide a measure of wind speed.

60. A system as claimed in any one of claims 31 to 59 adapted to use the range and velocity information for the collection of scatterers to provide a measure of air turbulence.