Abstract:
Chirped synthetic wave laser radar apparatus and methods are disclosed. In one embodiment, a system includes a laser source, a controller operatively coupled to the laser source and adapted to frequency-modulate first and second laser outputs, and an optical assembly. The optical assembly includes a plurality of reference channels adapted to receive a portion of a combined laser output and to provide a reference interference signal, and a signal channel having a focusing telescope adapted to focus and transmit at least part of the combined laser output onto the target, and to receive a scattered signal from target, and to provide a return interference signal. The system further includes a signal processing portion adapted to receive the reference interference signals and the return interference signal and to determine the distance to the target based on the reference and return interference signals.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
   This patent application is related to co-pending, commonly-owned U.S. patent application Ser. No. 11/014,919 entitled “Ultra-Linear Signal Processing for Radar and Laser Radar”, filed on Dec. 17, 2004, and U.S. patent application Ser. No. 11/016,623 entitled “Method and Apparatus for Combining a Targetless Optical Measurement Function and Optical Projection of Information”, filed Dec. 17, 2004, which applications are incorporated herein by reference. 
   FIELD OF THE INVENTION 
   This invention relates to radar systems, and more specifically, to chirped synthetic wave laser radar apparatus and methods used, for example, for manufacturing large scale objects. 
   BACKGROUND OF THE INVENTION 
   Radio detection and ranging (radar) may be used to detect, range, and map a wide variety of objects. For example, a weather radar system on an airplane can detect and range rain or other weather events, and a military fire control radar system can detect and track a military target, such as a ship or an aircraft. 
   Radar can also be used to range and map objects for manufacturing purposes. For example, laser radar is particularly well-suited for manufacturing large-scale objects (such as aircraft) because laser radar allows precise measurement over a large volume. In one approach, referred to as a chirped or Frequency Modulated-Continuous Wave (FMCW) radar, the radar frequency is modulated, as disclosed, for example, in U.S. Pat. No. 4,594,000 issued to Falk et al., incorporated herein by reference. Another approach, as disclosed in U.S. Pat. No. 5,371,587 issued to de Groot et al., uses a Chirped Synthetic Wavelength (CSW) method in combination with FMCW. 
   In a chirped radar, there is a time delay between the time when the signal is sent to an object and the time when the radiation scattered from the object is collected. As a result, there is a frequency difference between the radiation that is transmitted and the radiation that is collected. If these two signals with different frequencies are mixed, a beat frequency is observed. If the chirp is linear, then the beat frequency is proportional to the time delay and, therefore, to the range to the scattering object. If the chirp is not linear, then measuring range with a chirped radar entails measuring a sinusoidal signal that is varying in frequency (or, equivalently, in phase) in an environment of random noise. 
   Although desirable results have been achieved using prior art chirped radar systems, there is room for improvement. For example, prior art chirped radar systems, including those radar systems disclosed in the above-referenced patent issued to de Groot et al., typically include complex optical systems. These complex optical systems may adversely impact the cost and reliability of such prior art systems. 
   SUMMARY OF THE INVENTION 
   The present invention is directed to chirped synthetic wave laser radar apparatus and methods. Embodiments of apparatus and methods in accordance with the present invention may advantageously simplify the optical system of such radar systems, and may thereby reduce cost and improve reliability in comparison with prior art systems. 
   In one embodiment, a system for determining a distance to a target includes a laser source adapted to provide a first laser output and a second laser output, a controller operatively coupled to the laser source and adapted to frequency-modulate the first and second laser outputs, and an optical assembly adapted to receive and combine at least part of the first and second laser outputs into a combined laser output. The optical assembly includes a plurality of reference channels adapted to receive a portion of the combined laser output and to provide a reference interference signal, and a signal channel having a focusing telescope adapted to focus and transmit at least part of the combined laser output onto the target, and to receive a scattered signal from target, and to provide a return interference signal. The system further includes a signal processing portion adapted to receive the reference interference signals and the return interference signal and to determine the distance to the target based on the reference and return interference signals. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Embodiments of the present invention are described in detail below with reference to the following drawings. 
       FIG. 1  is a block diagram of a system for determining range to a target in accordance with an embodiment of the invention; 
       FIG. 2  is a block diagram of signal processing according to an embodiment of the present invention; 
       FIG. 3  is a top-level software block diagram of phase calculation according to an embodiment of the present invention; 
       FIGS. 4A–4D  are illustrations of pre-processing of samples according to an embodiment of the present invention; 
       FIGS. 5A and 5B  are illustrations of an exemplary time series interval and its Fourier transform; and 
       FIG. 6  is an illustration of an exemplary phase-versus-time plot derived from a time series. 
   

   DETAILED DESCRIPTION 
   The present invention relates to chirped synthetic wave laser radar apparatus and methods. Many specific details of certain embodiments of the invention are set forth in the following description and in  FIGS. 1–6  to provide a thorough understanding of such embodiments. The present invention may have additional embodiments, or may be practiced without one or more of the details described for any particular described embodiment. 
   In general, embodiments of the present invention may advantageously reduce the optical complexity of laser radar apparatus in comparison with the prior art. More specifically, embodiments of the present invention may eliminate certain components typically present in prior art chirped synthetic wave laser radar apparatus. Thus, by reducing the complexity of the optical system within the laser radar apparatus, embodiments of the present invention may provide improved reliability and reduced cost in comparison with prior art systems. 
   More specifically, embodiments of the present invention may combine aspects of chirped laser radar systems with synthetic wave distance measurements to provide highly accurate distance measurement. Chirped laser radar measurements may exhibit limited resolution for practical lasers, but provide an absolute measurement. On the other hand, synthetic wavelength methods generally provide improved resolution (depending on the chosen synthetic wavelength), but the result is ambiguous because the integer number of synthetic wavelengths must be known to have an absolute distance measurement. Embodiments of the present invention advantageously combine aspects of both chirped laser radar systems and synthetic wavelength distance measurements to achieve improved distance measurement performance over the prior art. 
     FIG. 1  shows a chirped synthetic wave laser radar system  10  in accordance with an embodiment of the invention. The radar system  10  includes a two-frequency laser source  12 , and a reference interferometer  44  including reference channels  44   a ,  44   b , and  44   c . In one particular embodiment, the system  10  has a maximum operating range of approximately 4 meters with a range resolution of approximately 0.02 mm. Another particular embodiment has a maximum operating range of approximately 8 meters with a range resolution of approximately 0.02 mm. In alternate embodiments, however, the system  10  may have other maximum operating ranges and range resolutions as desired for a particular application. Furthermore, the laser source  12  may include more than two lasers and the reference interferometer  44  may include more than three reference channels, if desired. 
   The system  10  is adapted to measure distance to a target  14 , including a non-cooperative target, that is, a target that does not include retro-reflectors or fiducials. With continued reference to  FIG. 1 , the laser source  12  includes a first laser source  12   a  and a second laser source  12   b . DC power sources  101   a  and  101   b  provide a DC bias current to the lasers  12   a  and  12   b  that operate at wavelengths that are different from each other. Given by way of nonlimiting example, the laser sources  12   a  and  12   b  may include distributed feedback (DFB) laser diodes. The laser sources  12   a  and  12   b  may have relatively high output power. Suitable embodiments of laser sources include, for example, model CQF-935/708 diodes commercially-available from JDS Uniphase Corporation of San Jose, Calif., and model TLB-6000 diodes commercially-available from New Focus, Inc. of San Jose, Calif. In further embodiments, the laser sources  12   a ,  12   b  may include external cavity laser diodes, fiber lasers, and any other suitable laser source. 
   Given by way of non-limiting example, the first laser source  12   a  suitably has a wavelength λ 1  of approximately 1550 nanometers (nm) and the second laser source  12   b  suitably has a wavelength λ 2  of approximately 1550.6 nm. The wavelengths λ 1  and λ 2  correspond to frequencies that differ from each other by around 100 GHz or so. While any wavelength may be selected as desired for a particular application, it is important that the wavelengths λ 1  and λ 2  be different from each other. This difference in wavelengths enables generation of an interference pattern that will be processed to determine range to the target  14 , as will be discussed below. 
   The first and second laser sources  12   a  and  12   b  are frequency-modulated by chirp generators  103   a  and  103   b , respectively. The chirp generators  103   a  and  103   b  may suitably provide a triangle-wave modulation to the bias currents that drive the laser sources  12   a ,  12   b . The lasers respond to the varying drive current by shifting in operating frequency. When the laser sources  12   a ,  12   b  are DFB lasers, modulation frequency of the triangle wave may be limited to approximately 3000 Hz. If external cavity lasers are used, the modulation frequency may be slower. An exemplary modulation frequency used with external cavity lasers is approximately 100 Hz. Output of the chirp generator  103   b  is supplied to an inverting amplifier  105 , which inverts and amplifies (e.g. by a factor of approximately 2) the triangle wave modulation. It will be appreciated that the inverted and amplified output from the inverting amplifier  105  advantageously causes the two beat frequencies from the two laser sources  12   a ,  12   b  to be far enough apart in a Fourier transform portion of the signal processing (described below) that they can be separated, allowing the frequencies and phases to be measured separately. 
   Output of the inverting amplifier  105  in turn is provided to the second laser source  12   b . A modulation current, such as a triangle wave from the chirp generator  103   a  and an inverted triangle wave from the inverting amplifier  105 , is added to the DC bias supplied by the DC power sources  101   a  and  101   b , respectively. A trigger  107  ensures simultaneous operation of the chirp generators  103   a  and  103   b . Because the frequencies of the laser sources  12   a  and  12   b  are modulated, the laser source  12  may be considered a chirped laser and, accordingly, the system  10  may be considered a chirped laser radar. 
   The beams from the laser sources  12   a  and  12   b  are sent through an optical fiber and are combined in a first splitter  40 . In this embodiment, the combined beam is sent from the first splitter  40  through an optical fiber to a second splitter  41 , where the combined beam is further combined with the output of a visible laser  43 . As shown in  FIG. 1 , in some embodiments, it may be desirable to include the output of the visible laser  43  so that the laser beam that is propagated to the target  14  is visible, such as may be desirable, for example, for persons working in a manufacturing environment. Alternately, the visible laser  43  (and the second splitter  41 ) may be eliminated. 
   As further shown in  FIG. 1 , the combined beam is sent from the second splitter  41  through an optical fiber to a third splitter  80 , which further splits the combined beam and routes a portion of the combined beam through an optical fiber  88 . As representatively shown in  FIG. 1 , a reflected portion  87  of the combined beam is reflected as a natural Fresnel reflection from a flat polished end  89  of the optical fiber  88 , and passes back along the optical fiber  88 . The end  89  of the optical fiber  88  may be intentionally adapted to provide the reflected portion  87  (e.g. as a local oscillator). Unless otherwise specified, various other fiber ends throughout the system  10  may be adapted to provide approximately no reflections to avoid undesirable noise and interfering signals. 
   As further shown in  FIG. 1 , a non-reflected portion exits from the optical fiber  88  and is focused and transmitted by an output telescope  86  to the target  14 . More specifically, in one particular embodiment, the output telescope  86  includes an objective lens  91  that receives an expanding beam  93  exiting from the end  89  of the fiber  88 , thereby eliminating the need for a diverging lens in the output telescope  86 . In alternate embodiments, however, the output telescope  86  may have both diverging and objective lenses. The output telescope  86  may also be adapted to provide approximately no reflections that might otherwise produce undesirable noise and interfering signals. An interference between the reflected portion  87  and the light scattered back to the system  10  by the target  14  is analyzed to determine the distance to the target  14 . 
   A photo detector  82  is also optically coupled to the third splitter  80 . Output of the photo detector  82  is provided to an input interface  21  of a processor  20 , where the output of the photo detector  82  may undergo an analog-to-digital conversion (ADC) and may be further processed as discussed below. The processor  20  may be any suitable signal processor, including, for example, a digital signal processor such as an Alacron Digital Signal Processor, a field programmable gate array (FPGA) with operations at up to around 3,000 points per second, and any other suitable processor or processing device. 
   The reflected portion  87  of the combined beam that reflects from the output telescope  86  back through the optical fiber  88  may be approximately four percent of the portion of the combined beam that reaches the output telescope  86 . Also, a return signal from the target  14  enters the optical fiber  88  via the output telescope  86 . The return signal from the target  14  and the natural, Fresnel reflection from the output telescope  86  combine to form an interference signal. The interference signal is sent through the optical fiber to the third splitter  80  and is detected by the photo detector  82 . The detected interference signal is then provided by the photo detector  82  to the processor  20  for processing as described below. 
   As mentioned above, the reference interferometer  44  includes reference channels  44   a ,  44   b , and  44   c , each reference channel including optical fibers of a known length. As will be discussed below, determining and comparing frequency of signals from the reference channels  44   a ,  44   b , and  44   c  with frequency of the interference signal advantageously enables embodiments of the present invention to determine range to the target  14 . 
   As further shown in  FIG. 1 , the first splitter  40  provides via an optical fiber a portion of the combined laser beams to a fourth splitter  48  that, in turn, provides the portion of the combined laser beams to the reference interferometer  44 . More specifically, a portion of the combined laser beams is supplied via an optical fiber to the reference channel  44   a  from the fourth splitter  48 . Another portion of the combined laser beams is supplied via an optical fiber from the fourth splitter  48  to a fifth splitter  68 . The fifth splitter  68 , in turn, supplies portions of the combined laser beams via optical fibers to the reference channels  44   b  and  44   c.    
   The reference channel  44   a  includes a sixth splitter  54  that receives the portion of the combined laser beams from the fourth splitter  48 . An optical fiber  60  with flat, polished ends  62  and  64  is optically coupled to the sixth splitter  54  at the end  62 . The optical fiber  60  has a predetermined, known length l 1 . The length l 1  is selected to be approximately around one-half the expected distance to the target  14 , that is, around one-half of the maximum length that is expected to be measured. For example, in one embodiment, the length l 1  is around 2 meters because the maximum range expected to be measured is around 4 meters. 
   A photo detector  56  is also optically coupled to the sixth splitter  54 . Output of the photo detector  56  is provided to the input interface  21  of the processor  20 . At the processor  20 , the output of the photo detector  56  is sampled, undergoes an analog-to-digital conversion (ADC), and is further processed as discussed below. 
   The portion of the combined beams is sent from the sixth splitter  54  through the optical fiber  60 . A natural, Fresnel reflection (e.g. approximately four percent) of the portion of the combined beam reflects from the end  62 . The rest of the portion of the combined beam exits the end  62  and is sent through the optical fiber  60  along its length l 1  to the end  64 . A natural, Fresnel reflection of the portion of the combined beam that has been sent to the end  64  reflects from the end  64 . The natural, Fresnel reflections from the ends  62  and  64  combine to form a reference interference signal. The reference interference signal is sent to the sixth splitter  54  and is detected by the photo detector  56 . The detected reference interference signal is provided by the photo detector  56  to the processor  20  for processing as described below. 
   The reference channels  44   b  and  44   c  are constructed in a similar manner. The reference channel  44   b  includes a seventh splitter  54 ′ and photo detector  56 ′, and an optical fiber  60 ′ with flat, polished ends  62 ′ and  64 ′. However, the optical fiber  60 ′ has a predetermined, known length l 2  that is different from the length l 1 . Likewise, the reference channel  44   c  includes an eighth splitter  54 ″ and photo detector  56 ″, and an optical fiber  60 ″ with flat, polished ends  62 ″ and  64 ″. However, the optical fiber  60 ″ has a predetermined, known length l 3  that is different from the lengths l 1  and l 2 . The lengths l 2  and l 3  are used to compute the integral phase for the reference length l 1 . The shorter of the lengths (computed from the difference between the lengths l 2  and l 3 ) is short enough such that the normal drift of the wavelength of the laser preferably causes less than one cycle change in the measured phase. In a particular embodiment, for example, the shorter of the lengths is selected to cause less than approximately one fourth of a cycle change in the measured phase. Then the longer length is chosen to provide a convenient frequency to be a substantial fraction of the length l 1 . In one specific embodiment, for example, the difference between the lengths l 2  and l 3  may be approximately 174 mm, and the length l 2  may be approximately 823.5 mm. 
   In yet another specific embodiment, two DFB laser diodes separated by approximately 90 GHz are used to generate the output, chirping in opposite directions with slopes differing by approximately a factor of two (i.e. an amplification factor by the inverting amplifier  105  of approximately two). The light is combined in a polarization-maintaining fiber using a conventional 50:50 splitter, and then split into four parts with more 50:50 splitters. A fiber length of a first one of the reference channels may be approximately 0.5 meters long, and a fiber length of a second one of the reference channels may differ from the fiber length of the first one of the reference channels by approximately 2 cm. A fiber length of a third one of the reference channels may be approximately 5 meters in length. In this embodiment, the reference interferometer provides a sequence of references composed of the difference between the fiber lengths of the first and second reference channels (i.e. approximately 2 cm), the fiber length of either the first or second reference channels (i.e. approximately 0.5 meters), and the fiber length of the third reference channel (i.e. approximately 5 meters). Proper sequencing of these references ensures that the system  10  can accommodate a range of laser variations normally encountered without losing track of the integer number of cycles. 
   Embodiments of the radar apparatus and methods in accordance with the invention may provide significant advantages over the prior art. For example, because the output beam transmitted to the target  14  is focused by the output telescope  86  rather than collimated, the system  10  may operate properly at longer ranges in comparison with conventional chirped synthetic wave radar systems. Embodiments of the invention also have more simplified optics in comparison with conventional chirped synthetic wave radar systems. For example, in comparison with conventional systems, such as those systems disclosed in U.S. Pat. No. 5,371,587 issued to de Groot et al., there is no need for a phase modulator in the output channel, and no rectifier in the analog signal electronics. Therefore, the complexity of the optics of embodiments of the invention are simplified, and cost and reliability are improved. 
   Embodiments of the invention provide signal processing that determines parameters related to phase and/or frequency of sinusoidal signals in the presence of non-linearities in the frequency modulation of the source, such as laser sources of a laser radar, that may be more accurate than the prior art. According to embodiments of the invention, use of time-resolved frequency analysis permits comparing results between a known, reference length and the distance to the target  14  that is desired to be measured. Advantageously, this approach is applicable to frequency-based implementations, such as a chirped laser radar, as well as phase-based implementations, such as synthetic wave interferometry. 
   Signal processing routines described herein may suitably be executed by the processor  20  responsive to commands or instructions contained in a software program. The software program may be a computer software program product with executable computer software program code stored on storage media, such as without limitation a CD-ROM, a flash disk, an optical disk, a floppy disk, or the like, and loaded into random-access-memory (RAM) of the processor  20 . Alternately, the software program may be burned into non-volatile memory, such as electrically-erasable programmable read-only memory (EEPROM), flash EEPROM, or the like, of the processor  20 , if applicable. 
   Referring now to  FIG. 2  and by way of overview, an exemplary routine  100  processes signals according to an embodiment of the invention. At a block  102 , signal channel data for the interference signal from the photo detector  82  (referred to herein as a “signal channel”) is input. At a block  104 , reference interference signal data from the reference channel  44   a  is input. Similarly, at a block  106 , reference interference signal data is input from the reference channel  44   b , and at a block  108 , reference interference signal data is input from the reference channel  44   c.    
   At a block  110 , an average phase Ø 0  is computed for the interference signal from the signal channel, and average phases Ø 1 , Ø 2 , and Ø 3  are computed for the reference interference signals from the reference channels  44   a ,  44   b , and  44   c , respectively. At the block  110 , a frequency ratio R is computed between the interference signal and the reference length l 1  (described above), and also a quality factor Q of the interference signal is computed, for the signal channel and the reference channel  44   a.    
   Although phase and frequency may not be well-defined quantities for a time-varying single tone, the slope of a plot of phase versus time or the average phase value may be repeatable and may be sufficiently precise quantities. According to embodiments of the invention, in the case of a chirped laser radar that uses a reference length (such as the reference channels  44   a ,  44   b , and  44   c ), comparison of the slopes or the average phases advantageously may provide a measure of distance to the target  14  that may be as accurate as if the frequency of the chirp were completely linear. 
   Phase may be measured as a function of time within a signal that is composed of narrow bandwidth sinusoids in random noise. A measurement indicative of frequency, referred to simply as “frequency” for sake of clarity, may be derived as the slope of the phase-versus-time function, and phase may be defined as the average phase over the measured time interval. Frequency in this case refers to the frequency term in a cosine function. Because the frequency of the signal typically varies, there is an array of frequency terms. According to embodiments of the invention, a linear fit through the phases yields a measurement indicative of frequency. Measuring this quantity that is indicative of frequency and then comparing that quantity between the signal channel and the reference channel can yield stable results. Advantageously, uncertainty in measurement of a varying signal in random noise may be reduced over conventional measurement techniques that perform a Fourier transform over the entire time interval of the signal. 
   As further shown in  FIG. 2 , at a block  112 , range and measurement quality are computed from the average phases Ø 0 , Ø 1 , Ø 2 , and Ø 3 , the ratio R, and the quality factor Q. Details regarding the processing blocks will be explained below. It will be appreciated that, in the following discussion and accompanying figures, the processing of a single frequency is shown and described, while in actual operation, embodiments of the invention simultaneously process two frequencies (one from the first laser source  12   a  and another from the second laser source  12   b ). For the sake of brevity and clarity, however, in the following, the processing of a single frequency is described and shown. 
   Referring additionally to  FIG. 3 , at the blocks  102 ,  104 ,  106 , and  108  data is sampled over one-half cycle of modulation (corresponding to a monotonic portion of the triangle wave generator&#39;s signals). Advantageously, a group of samples, referred to as a subinterval or a subsample, overlaps adjacent groups of samples (that is, adjacent subsamples). It is the subsample on which a Fourier transform is performed to extract frequency and phase. This approach presents two competing issues. First, it is desirable that the time centers of the subsamples be close together because the integral phase is estimated from the measured frequency. The shorter the time interval, the more likely that a mistake is not made (such as slipping a modulation cycle). Second, if the subsample is larger, the accuracy with which frequency and phase can be determined is better. Overlapping advantageously affords the benefits of shorter time intervals (thereby reducing probability of mistakes) as well as the benefits of longer time intervals (thereby increasing accuracy), at the cost of more computation. Use of subintervals also permits more than one sinusoid in the signal (assuming that spectral peaks are sufficiently well-separated). 
   In a particular, non-limiting embodiment, for example, forty-three subsamples are taken. Each subsample includes 512 sample points and has a seventy-five percent overlap of common sample points with adjacent subsamples. However, it will be appreciated that, in alternate embodiments, any number of sample points and any amount of overlap may be selected as desired for a particular application. For example, by selecting a step size of 128 points (25% of the subsample size), it follows that a subsample  114   a  includes sample points  0 – 511 ; a subsample  114   b  includes sample points  127 – 639 ; a subsample  114   c  includes sample points  255 – 767 ; and so on through a subsample  114   aq  (that is, the forty-third subsample) that includes sample points  5376 – 5887 . 
   At a block  116  ( FIG. 3 ), the sample points in the subsamples  114   a – 114   aq  are preprocessed. Referring additionally to  FIGS. 4A–4D , details are set forth regarding the preprocessing performed at the block  116 . A time series  118  ( FIG. 4A ) of a sinusoidal signal is representative of any one of the subsamples  114   a – 114   aq  ( FIG. 3 ). The time series  118  may be the interference signal from the signal channel or any of the reference interference signals from any of the reference channels  44   a ,  44   b , or  44   c.    
   The time series  118  is filtered (or windowed), thereby resulting in a filtered time series  120  ( FIG. 4B ). Filtering advantageously damps down side lobes. Any filter function may be applied as desired, including without limitation a Kaiser-Bessel filter, a Chebycheff filter, a Hamming filter, or the like. In one embodiment, a Kaiser-Bessel filter is applied because a Kaiser Bessel allows the width to be tuned smoothly. The Kaiser-Bessel filter window may be implemented as a look-up table resident in storage (not shown) in the processor  20 . Given by way of non-limiting example, the look-up-table may implement weighting coefficients for the Kaiser-Bessel filter function as 8-bit integers. 
   A zero-padded time series  122  ( FIG. 4C ) is created by adding sample points that are all zeroes onto the end of the time series  120  ( FIG. 4B ) (referred to as “zero padding”). The number of zero sample points may be the same as the number of sample points in the subsample that makes up the time series  120 . Given by way of non-limiting example, 512 zero sample points may be added onto the end of the time series  120 , thereby populating the time series  122  with 1,024 sample points. Zero padding the time series  120  to create the time series  122  increases resolution because the number of sample points is increased. In the non-limiting example illustrated herein, the time series  122  contains twice the number of sample points as does the time series  120 . 
   The zero-padded time series  122  is rotated by a predetermined amount, thereby resulting in a rotated time series  124  ( FIG. 4D ). Any amount of rotation may be used as desired for a particular application. Given by way of non-limiting example, the zero-padded time series  122  has been rotated by around twenty-five percent or so to create the rotated time series  124 . It is noted that the middle of the function of the rotated time series  124  is at the ends of window. The data is rotated to determine the phase at the center of the subsample (where it has better noise characteristics). A Fourier transform evaluated for phase determines phase at the beginning of the time series being evaluated. Rotating the data puts the middle of the time series and the point at which the phase is being measured at the same spot—that is, the beginning of the time series. Putting the phase at the center of the time series reduces noise because there is less variation over a set of identical samples than measurements made at either the beginning or the end of the time series. 
   Referring back to  FIG. 3 , at a block  126  a Fourier transform is performed on the rotated time series  124  ( FIG. 4D ). The Fourier transform may be implemented as a fast Fourier transform (FFT) in a known manner. It will be noted again that the original interference signal has been sampled in overlapping subsamples—such as, for example, the forty-three overlapping subsamples  114   a – 114   aq.    
   For example, referring additionally to  FIGS. 5A and 5B , a subinterval  114   b ′ is a graphical illustration of interference signal amplitude versus time that is sampled in the 512 samples of the subsample  114   b  ( FIG. 3 ). A subinterval  114   c ′, that overlaps the subinterval  114   b ′, is a graphical illustration of interference signal amplitude versus time that is sampled in the 512 samples of the subsample  114   c  ( FIG. 3 ). A graph  128   b ′ illustrates a Fourier transform of the rotated time series  124  derived from the subinterval  114   b ′ and a graph  128   c ′ illustrates a Fourier transform of the rotated time series  124  derived from the subinterval  114   c′.    
   Because the Fourier transform is performed on each rotated time series  124 , and each rotated time series  124  represents only one subsample, the Fourier transform is performed on only a subinterval of the original time-sampled interference signal. Performing the Fourier transform on the subinterval advantageously results in a Fourier transform peak that is significantly narrower than broad Fourier transform peaks performed on entire intervals of signals as known in the prior art. This subinterval Fourier transform processing advantageously results in more accurate determinations of phase and/or frequency than processing of entire signal intervals according to the prior art. 
   The Fourier transform may be performed as an FFT in any acceptable manner as desired for a particular application. Imaginary values are input as zeroes. Given by way of non-limiting example, the FFT may use 1024 floating point input values with 64-bit floating point arithmetic. As a further example, the FFT may use 512 20-bit integer input values with 32-bit fixed point arithmetic. 
   Referring back to  FIG. 3 , at a block  130  phase at peak frequency is computed. From the Fourier transform, phase at the center of the subinterval is obtained using peak finding and phase interpolation methods. In one presently preferred embodiment, the approach for determining phase is as follows. Given real and imaginary FFT results R(x) and I(x), power is computed:
 
 P ( x )= R ( x )* R ( x )+ I ( x )* I ( x )  (1)
 
Indices of two highest local maxima values are found where indices are each greater than 14 and differing by at least 14 in magnitude (the preceding values of 14 are replaced with 5 for signals from reference channels  44   b  and  44   c ). At each index, peak frequency and fractional phase are computed. Finally, total phase is computed.
 
   Peak frequency is computed as follows. Given power P(x) and a local maximum index i, peak frequency is computed from a parabolic fit of power on either side of the index i:
 
 dP ( i+ 1)= P ( i+ 1)− P ( i )  (2)
 
 dP ( i− 1)= P ( i− 1)− P ( i )  (3)
 
 f=i− ( dP ( i+ 1)− dP ( i− 1))/( dP ( i+ 1)+ dP ( i− 1))/2  (4)
 
   Fractional phase is computed as follows. Given real and imaginary FFT results R(x) and I(x) and given peak frequency f, fractional phase is computed via linear interpolation:
 
 j =Floor( f ) and  k =Ceil( f )  (5)
 
 R $= R ( j )+( R ( k )− R ( j ))*( f−j )  (6)
 
 I $= I ( j )+( I ( k )− I ( j ))*( f−j )  (7)
 
Φ=−arctan 2( I $, R $)/2π  (8)
 
Combined values for frequency and phase are next computed, and then total phase is computed. Given peak frequencies f 1  and f 2 , associated with the two local maxima previously determined, and given corresponding fractional phases Φ 1  and Φ 2 , combined frequency and phase are computed:
 
 f=f   1   +f   2  (units are cycles/transform)  (9)
 
Φ=Φ 1 +Φ 2  (units are cycles)  (10)
 
Total phase is computed by adding integer cycles relative to phase from preceding subsample:
 
Ø=Φ+Round(Ø$−Φ+( f $+ f )/2α)  (11)
 
where
         f$=combined frequency from preceding subsample;   Ø$=total phase from preceding subsample;   initial value of f$ and Ø$ are zero; and   α=transform size/step size (units are steps/transform).       

   Referring back to  FIG. 3 , at a block  132  average phase and average frequency is computed from the total phases that have been previously computed as described above by equations (1)–(11). Given total phases Ø(x) and where x=0 . . . n−1 (where n=number of subsamples), average phase is computed:
 
Ø=ΣØ( x )/ n   (12)
 
   Referring additionally to  FIG. 6 , a plot  134  of phase versus time has a slope with substantially little variation. As such, a linear fit through the phase data can be made and a frequency can be associated with the slope of the linear fit through the phase data. Average frequency for the signal channel interference signal and the reference interference signal from the first reference channel  44   a  is computed from slope of phase as follows.
 
δ=Σ(Ø( x )* x )−Ø*β (units are arbitrary)  (13)
 
where
         β is a constant based on step size and n.
 
Average frequency is not computed for the second and third reference channels  44   b  and  44   c  because frequency is not used to estimate the integer phase for the reference channels. The integer phase is estimated from the known ratios of the lengths l 1 , l 2 , and l 3 . It is only on the measured length to the target that the integer phase is estimated from the chirp frequencies.
       

   The ratio R of average frequencies is computed as follows:
 
 R=δ   0 /δ 1  (unitless)  (14)
 
   Referring back to  FIG. 2 , in an exemplary embodiment range is computed at the block  112  using an iterative process as follows. Given average phases for the second and third reference channels  44   b  and  44   c  and given lengths of the second and third reference channels  44   b  and  44   c , an estimate is made for synthetic wavelength λ. It will be noted that different values are used for up-chirp and down-chirp data—one of which will be negative. 
   A difference in average phases is used to make first refinement:
 
Ø 23 =(Ø 2 −Ø 3 )  (15)
 
Length 23 =(Length 2 −Length 3 )  (16)
 
λ′=Length 23 /(Ø 23 +Round(Length 23 /λ−Ø 23 ))  (17)
 
   Average phase for the third reference channel  44   c  is used to make a second refinement of synthetic wavelength:
 
λ″=Length 3 /(Ø 3 +Round(Length 3 /λ′−Ø 3 ))  (18)
 
   Given average phases for the interference signal for the signal channel and for the reference interference signal for the first reference channel  44   a , and given length of the first reference channel  44   a , and given the ratio R of average frequencies, average phase for the first reference channel  44   a  is used to make a final refinement of synthetic wavelength:
 
λ$=Length 1 /(Ø 1 +Round(Length 1 /λ″−Ø 1 ))  (19)
 
   The average phase for the signal channel and the ratio R of average frequencies are used to compute range:
 
Range=(λ$*(Ø 0 +Round(Length 1   *R /λ$−Ø 0 )))/2  (20)
 
However, it will be appreciated that a ratio of the phases is also directly proportional to a ratio of distance to the target and length of the first reference channel  44   a.  
 
   In an alternate embodiment of a method of processing signals to determine the Range from the system  10  to the target  14 , a different method of determining average phases and average frequencies, and thus computing Range using Equation 20, may be used. More specifically, in an alternate embodiment, an initial estimate is made of the synthetic wavenumber expressed in round trip, K 0 . This initial estimate is used to estimate the integer part of the phase of the shortest interferometer, which in one particular embodiment is the difference in length of the first two reference channels (e.g. ˜20 mm in length). The round function may then be used to estimate the phase according to the following equation:
 
 p 23=round( p 23exp− p 23 meas )+ p 23 meas   (21)
 
   The length of the difference is L 23 , and p 23 exp=K 0 *L 23  is the estimated phase, p 23  is the calculated phase, and p 23 meas is the phase measurement from the FFT process. Next, the phase of the next longer interferometer whose length is L3 and whose phase is p 3  is calculated as follows:
 
 p 3=round( p 23 meas*L 3/ L 23− p 3 meas )+ p 3 meas   (22)
 
   Similarly, the longest reference phase p 1  may be computed. In the estimate of the signal channel range L 0 , the chirp information may be used, including the frequency for the signal channel f 0 , and the frequency for the longest reference interferometer f 1 . The round trip range L 0  of the signal channel is then estimated as follows:
 
 L 0=(round( p 1* f 0/ f 1− p 0 meas )+ p 0 meas )* L 1  (23)
 
where L 1  is the length of the longest reference interferometer. This alternate signal processing procedure encodes the synthetic wavelength in the phase p 1 , similar to the signal processing procedure described above. Again, using the average phases for the interference signal for the signal channel, and for the reference interference signal for the first reference channel  44   a , and given length of the first reference channel  44   a , and given the ratio R of average frequencies, average phase for the first reference channel  44   a  is used to make a final refinement of synthetic wavelength. The average phase for the signal channel and the ratio R of average frequencies are then also used to compute range using Equation 20 above.
 
   While embodiments of the invention have been illustrated and described above, many changes can be made without departing from the spirit and scope of the invention. Accordingly, the scope of the invention is not limited by the disclosure of these embodiments. Instead, the invention should be determined entirely by reference to the claims that follow.