Abstract:
A coherent anti-Stokes Raman spectroscopy (CARS) system comprises a laser light source for emitting pulsed light, a dichroic beam splitter for splitting a light pulse from the light source into a pump pulse and a Stokes pulse and directing these pulses along respective distinct paths, chirping means, e.g. dispersive glass blocks for chirping the pump and Stokes pulses, directing means for directing the chirped pump and Stokes samples to a sample in time overlap, and detecting means for detecting light stimulated from the sample by the interaction of the pump and Stokes pulses. The system may comprise a reflector connected to a linear motor, for adjusting the period between the arrival at the sample of the starts of the chirped pump and Stokes pulses. The system may further comprise a pulse replicating unit for converting a pulse from the light source into a plurality of pulses distributed in time.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a national phase application of International Application No. PCT/GB2010/050473, filed Mar. 19, 2010, claiming priority to Great Britain Application No. 0904739.0, filed Mar. 19, 2009, both of which are incorporated by reference herein in their entirety. 
     FIELD 
     The invention relates to the field of probing material with electromagnetic radiation to acquire information about the material. 
     BACKGROUND 
     Coherent anti-Stokes Raman spectroscopy (CARS) is a known technique for investigating the properties of materials such as biological cells. In a typical CARS system, a sample is illuminated with a pump beam and a Stokes beam and responds by emitting anti-Stokes radiation. A brief, classical (as opposed to quantum-mechanical) description of the physics of CARS will now be given. 
     Consider a molecule having a vibrational mode with a resonant frequency of ω v . If the frequencies of the pump beam ω p  and the Stokes beam ω s  are such that ω p −ω s =ω v , then the molecule will respond by emitting radiation forming a CARS beam at frequency ω c =ω p +ω v  that can then be detected. 
     Existing CARS systems utilise separate pulsed lasers to provide the pump and Stokes beams. These beams must be aligned optically and made incident upon the same volume within the target sample and the pulses from the two lasers must arrive at that volume at the same time. CARS systems of this type require expert attention in order to achieve the aforementioned spatial and temporal alignment of the delivery of the laser radiation and are often fragile in that this alignment can easily be upset (e.g., by physical shock). However, it is known to use a single laser source to provide both the pump and Stokes beams, as reported in for example in Physical Chemistry Chemical Physics 10, 609 (2008) and the documents referenced therein. 
     In order to target a vibrational mode of interest within a sample under analysis that has a resonant frequency ω v , the pump and Stokes beams must be tuned accurately to achieve ω p −ω s =ω v . Typically, this tuning is achieved by using diffraction gratings and liquid crystal arrays or similar to select desired probed CARS frequencies from broadband laser emissions. Again, such tuning arrangements can be awkward and sensitive to disruption. 
     SUMMARY 
     The invention relates to Coherent anti-Stokes Raman spectroscopy (CARS). A single light source may be used to generate pump and Stokes beams of interrogating light. Pump and Stokes beams may be chirped in various ways to produce various effects in the CARS light that is produced. Components of pulses of interrogation light may be delayed relative to others to allow multiple investigations to be performed in the same apparatus. Fourier analysis may be used to derive differential results from the multiple investigations. The invention is defined in the appended claims to which reference should now be made. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       By way of example only, certain embodiments of the invention will now be described by reference to the accompanying drawings, in which: 
         FIG. 1  is a block diagram schematically illustrating a CARS system; 
         FIG. 2  is a graph of intensity versus frequency for the broadband laser used in the CARS system of  FIG. 1 ; 
         FIG. 3  is a graph of intensity versus frequency for the laser in the CARS system of  FIG. 1  after filtering has been applied; 
         FIG. 4  is a graph of frequency versus time for various pulses in the CARS system of  FIG. 1 ; 
         FIG. 5  is provides various graphs relating to pulses within the CARS system of  FIG. 1  under operating parameters different to those pertaining in  FIG. 4 ; 
         FIG. 6  is a block diagram schematically illustrating a variant of the CARS system of  FIG. 1 ; 
         FIG. 7  is a graph of intensity versus time for various pulses in the CARS system of  FIG. 6 ; 
         FIG. 8  shows two graphs of pulses of CARS light, before and after compensation, respectively; 
         FIG. 9  is a block diagram schematically illustrating a variant of the CARS system of  FIG. 6 ; 
         FIG. 10  is a block diagram schematically illustrating the pulse replicating unit within the CARS system of  FIG. 9 ; 
         FIGS. 11   a  to  11   h  are graphs showing the polarisation of pulses within the pulse replicating unit of  FIG. 10 ; 
         FIG. 12  is a graph illustrating the effect of the pulse replicating unit of  FIG. 10 ; and 
         FIG. 13  is a block diagram schematically illustrating a circuit for processing an output signal from a photomultiplier tube in the microscope of the CARS system of  FIG. 9 . 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  illustrates a CARS system  10  that comprises a chirp unit  12  that modifies broadband light from a laser  14  to create interrogation light that is delivered to a microscope  16  to stimulate a target sample (not shown) within the microscope  16  to emit CARS light. The laser  14  emits linearly polarised light in pulses of duration of less than 10 fs and consisting of broadband light covering a wavelength range of 700 to 950 nm. The microscope  16  is a standard confocal fluorescence microscope. The nature of the chirp unit  12  will now be discussed. 
     In the chirp unit  12 , light from the laser is incident upon a dichroic beam splitter  18  that splits the laser light into two beams  20  and  22 , each containing a different sub-band of the frequencies contained in the laser emissions. Beam  20  shall be called the Stokes beam and beam  22  shall be called the pump beam. From the dichroic beam splitter  18 , the Stokes beam  20  passes through a dispersive glass block  24 , reflects from a retroreflector  26  of corner cube type, reflects again from the dichroic beam splitter  18 , passes through a further dispersive glass block  28  and enters the microscope  16 . From the dichroic beam splitter  18 , the pump beam  22  passes through a dispersive glass block  30 , reflects from a retroreflector  32  of corner cube type, passes through the dichroic beam splitter  18 , passes through the dispersive glass block  28  and enters the microscope  16 . The dichroic beam splitter  18  is positioned such that the pump and Stokes beams  22  and  24  enter the microscope  16  along the same optical path. 
     The retroreflector  32  is mounted on a linear motor  34 . The motor  34  can move the retroreflector  32  back and forth along the optical path from the laser  14  to lengthen or shorten the travel time from the laser  14  to the microscope  16  of a pulse in the pump beam  22 . The glass blocks  24 ,  28  and  30  cause dispersion in the laser pulses. That is to say, they delay the different frequencies of the laser pulses by different amounts of time. The amount of dispersion that the blocks  24 ,  28  and  30  are designed to cause will shortly be described. 
       FIG. 2  illustrates the spectrum of a pulse from the laser  14  and  FIG. 3  illustrates the filtering effect of the dichroic beam splitter  18 . In  FIG. 3 , the spectrum of  FIG. 2  is overlaid as a dashed outline for comparison purposes and the spectra of the Stokes and pump beams  20  and  22  are indicated  38  and  36 , respectively. A laser pulse that passes through the dichroic beam splitter  18  is divided into a “Stokes pulse” and a “pump pulse”. The Stokes pulse is the part of the laser pulse that has spectrum  38  and forms part of the Stokes beam  20 . The pump pulse is the part of the laser pulse that has spectrum  36  and forms part of the pump beam  22 . 
       FIG. 4  shows the effect of the glass blocks  24 ,  28  and  30  on pair of Stokes and pump pulses  40  and  42  derived from the same laser pulse.  FIG. 4  shows the pulses  40  and  42  in the form in which they enter the microscope  16  for application to the target sample. The glass blocks  24  and  28  are designed to have a cumulative dispersive effect on the Stokes pulse  40  that causes that pulse to undergo a linear chirp of frequency versus time with a particular gradient. The glass blocks  30  and  28  are designed to have a cumulative dispersive effect on the pump pulse  42  that causes that pulse to undergo a linear chirp of frequency versus time with a gradient substantially equal to the gradient of the Stokes pulse chirp. As can be seen in  FIG. 4 , the lowest frequency components of the Stokes and pump pulses  40  and  42  reach the microscope at the same time. This alignment is achieved by adjusting the position of retroreflector  32  to adjust the travel time of the pump pulse  42  back to the splitter  18  relative to the travel time of the Stokes pulse  40  back to the splitter  18 . 
       FIG. 4  also shows the pulse  44  of CARS light that is emitted by the target sample in response to the Stokes and pump pulses  40  and  42 . At all times, the instantaneous frequency difference (IFD) between the Stokes and pump pulses  40  and  42  is constant. The CARS pulse  44  corresponds to a vibrational mode in the target sample whose resonant frequency ω v  is equal to the IFD. Since the CARS pulse  44  corresponds to a single vibrational mode in the target sample, it suffices to detect the CARS pulse  44  with a simple photomultiplier tube (not shown) within the microscope  16 . The microscope  16  also includes a filter (not shown) for rejecting any light emanating from the sample whose frequency falls within the bandwidth of the laser  14 . 
       FIG. 5  illustrates the effect of varying the travel time of the pump beam  22  using the motor  34 . For ease of reference,  FIG. 5  includes a reproduction, indicated  46 , of the spectrum of  FIG. 3  and a reproduction, indicated  48  of the graph of  FIG. 4 . In graph  48 , the timing relationship of the Stokes and pump pulses  40  and  42  is indicated by τ, which is a measure of time elapsing between the arrival at the microscope  16  of the low frequency end of chirped pump pulse  42  and the arrival of the high frequency end of the Stokes pulse  40 . The IFD is also shown in graph  48 . The graph indicated  50  shows the effect of reducing τ by moving the retroreflector  32 . With τ reduced, it is apparent that the IFD is still constant but has a lower value. The CARS pulse that is produced in this situation is indicated  52 . 
     Thus, the retroreflector  32  can be moved backward or forwards along the path of the pump beam  22  as necessary to tune the IFD to correspond to the resonant frequency ω v  of a vibrational mode within the target sample that the user wishes to investigate. The selection of the desired resonant frequency ω v  is achieved relatively easily by operating the motor  34  and the use of a retroreflector  32  prevents minor irregularities in the motion imposed by the motor  34  from causing misalignment of the light beams. 
       FIG. 6  illustrates a CARS system  54  that is a variant of CARS system  10  of  FIG. 1 . Elements in  FIG. 6  that have been carried over from  FIG. 1  retain the same reference numerals and their nature and purpose will not be described again in detail. A beam splitter  56  diverts part of the output of the laser  14  away from the chirp unit  12  to form a beam that is reflected from a mirror  58  and then focussed by a lens  60  into a small volume within non-linear element  62  such as a sapphire plate or a high refractive index liquid. Light emerging from the focal volume within the non-linear element  62  results from a third-order mixing process within the non-linear element  62  (e.g. the optical Kerr effect). Light emerging from the focal volume within the non-linear element  62  is then focussed back into a beam by lens  64 . The beam from lens  64  is then reflected from mirror  66  and into microscope  68  as a reference beam. 
     The microscope  68  includes an objective lens  70  for focussing the Stokes and pump pulses from the chirp unit  12  into a volume within the sample  72 . A further objective lens  74  collects CARS pulse light from the targeted volume within the sample  72  and projects it as a beam onto a beam splitter  76 . Also incident upon beam splitter  76  is the reference beam from the non-linear element  62 . 
     Some (ideally half) of the light from the objective lens  74  is transmitted through the beam splitter  76  to a prism  78  and some of the light from the reference beam is reflected from the beam splitter  76  to the prism  78 . The beam emerging from the prism  78  is focussed by a lens  80  and is divided into two orthogonally polarised components by polarising beam splitter  82 . The polarised components are then detected by respective line scan cameras  84  and  86  lying in the image plane of the lens  80 . The prism  78  creates a wavelength dispersion in the light received from the beam splitter  76  and the lens  80  translates the wavelength dispersion into a range of positions along each of the line scan cameras  84  and  86 . 
     Some (ideally half) of the light from objective lens  74  is reflected by the beam splitter  76  to a prism  88  and some of the light from the reference beam is transmitted through the beam splitter  76  to the prism  88 . The beam emerging from the prism  88  is focussed by a lens  90  and is divided into two orthogonally polarised components by polarising beam splitter  92 . The polarised components are then detected by respective line scan cameras  94  and  96  lying in the image plane of the lens  90 . The prism  88  creates a wavelength dispersion in the light received from the beam splitter  76  and the lens  90  translates the wavelength dispersion into a range of positions along each of the line scan cameras  94  and  96 . The polarised components travelling to line scan cameras  86  and  96  have parallel polarisations. 
     The interference between CARS light and reference beam creates a spectral intensity interference pattern on each line scan camera  84 ,  86   94  and  96 . The images from a pair of cameras receiving the same polarisation (e.g. cameras  84  and  94 ) are subtracted from one another to isolate the interference pattern (spectral interferogram) for that polarisation, and to eliminate the individual spectra of the CARS light and reference beam (the individual spectra of the CARS light and the reference beam can be detected on the line scan cameras  84 ,  86 ,  94  and  96  by blocking the unwanted one of the reference beam or the CARS light). From the spectral interferogram, the spectral amplitude and phase of the CARS light can be retrieved by spectral interferometry (J. Opt. Soc. Am. B 12, 2467 (1995)). For this, we have to adjust the arrival time (by the optical path length) of a pulse in the reference beam to be before the corresponding CARS pulse such that there is no significant temporal overlap between the reference pulse and the CARS signal. (Typically, we would use about 0.5 ps between the reference pulse and the beginning of the corresponding CARS pulse in the system shown in  FIG. 6 . Choosing a much shorter value results in overlap, and choosing a much longer value reduces the temporal range over which the CARS can be retrieved from the interferogram for a given spectral resolution.) Thus, the microscope  68  is able to recover amplitude and phase information for the CARS light from the target volume within the sample  72 . This ability enables more sophisticated measurements to be made when certain adjustments are made to the chirp unit  12 , as will now be explained. 
     Specifically, the glass blocks  24 ,  28  and  30  are redesigned such that, although both the Stokes and pump beams are still given linear chirps, the rate of change of frequency of a Stokes beam pulse is now very different to the rate of change of frequency of a pump beam pulse. The Stokes beam pulses are chirped only slightly, in order to reduce the peak power applied to the sample material. On the other hand, the pump beam pulses are strongly chirped such that the frequencies in a pump beam pulse arrive at the sample over a relatively long period of time, comparable to the vibrational dephasing times. The effect of these changes to the chirp unit  12  is illustrated in  FIG. 7 . In addition, that diagram illustrates the option of redesigning the dichroic beam splitter  18  to use a smaller frequency sub-band for the pump beam than previously. This sub-band is located at the upper end of the band of output frequencies of the laser  14  such that a relatively large central sub-band of the band of output frequencies of the laser  14  is not used to illuminate the sample in the microscope  16 . This reduces the power to which the sample material is exposed and therefore reduces the risk of damaging the sample material. 
       FIG. 7  shows in graph  98  the sub-bands of the output band of the laser  14  that are now used for the Stokes and pump beams. The dashed line represents, as in  FIG. 3 , the band of output frequencies of the laser  14 . The adjusted sub-band that is allocated to the pump beam is indicated  99 . It will be apparent that the gap between sub-band  99  and the sub-band  36  that is used for the Stokes beam is now wider than the gap between sub-bands  38  and  36  in  FIG. 3 , representing a reduction in the power that is applied to the sample achieved through the optional redesign of the dichroic beam splitter  18 .  FIG. 7  also provides a graph  100  illustrating the modified forms now taken by a Stokes pulse  102  and a pump pulse  104  derived from the same pulse from the laser  14 . 
     With the retroreflector  32  positioned such that the Stokes and pump pulses  102  and  104  begin to arrive at the same time, it is apparent that, over the duration of the Stokes pulse  102 , the IFD varies over a range from a maximum value, IFD max , to a minimum value, IFD min . Since the IFD varies over a range, the pump and Stokes pulses can therefore excite CARS light from different vibrational modes of the sample material having different resonant frequencies in the range between IFD max  and IFD min . Thus, CARS light produced in response to pulses  102  and  104  consists of a collection of CARS pulses  106  to  110  that each relate to a different resonant frequency of the sample material. Each of the CARS pulses  106  to  110  endures for a period of time determined by the coherence time of its vibrational mode. The vibrational coherence time decreases from pulse  106  to pulse  108  to pulse  110 . 
     The CARS light gathered by objective  74  in response to Stokes pulse  102  and pump pulse  104  is shown again in graph  112  in  FIG. 8 . Since the microscope  68  detects the CARS light in terms of its amplitude and phase, mathematical techniques such as those described in OPTICS LETTERS 31, 1543 (2006) can be applied to mathematical data representing the CARS light detected by the microscope  68  in order to flatten the slopes of pulses  106  to  110  that are due to the chirping of the pump pulse  104 . This recovers a spectrum as shown in graph  114  in which the different vibrational modes that have been excited within the sample can be distinguished: pulses  106  to  110  have been flattened into pulses  116  to  120 , respectively. Specifically, the spectral of the temporal CARS response can be retrieved in amplitude and phase, which can be used to retrieve the chemical composition by linear decomposition, as opposed to measuring the CARS intensity only. 
     Another CARS system  122  is shown in  FIG. 9 . CARS system  122  is a variant of CARS system  10  in which a pulse replicating unit  124  has been inserted between the laser  14  and the chirp unit  12 . The pulse replicating unit  124  is shown in greater detail in  FIG. 10 . 
     As shown in  FIG. 10 , the beam from the laser  14  enters the pulse replicating unit  124  and passes through a half wave plate  126 . The laser beam then proceeds to a polarising beam splitter  128  which splits the laser beam into orthogonally polarised components. One of these components is a “transmitted component” that is transmitted through the polarising beam splitter  128  to a second polarising beam splitter  130 . The other component is a “reflected component” that is reflected through a dispersive glass block  132  and is then reflected by a mirror pair  134  to the second polarising beam splitter  130 . The half-wave plate  126  is orientated to rotate the linear polarization of the input laser beam to give desired relative intensities to the transmitted and reflected components produced by the polarizing beam splitter  128 . The second polarising beam splitter is orientated to transmit the transmitted component and to reflect the reflected component to travel in the same direction. The recombined polarisations of the laser beam then travel from the polarising beam splitter  130  to a half wave plate  136 . The polarising beam splitters  128  and  130 , the glass block  132  and the mirror pair  134  constitute a first delay arm  138  that delays the reflected component of the laser beam by an amount T 1  relative to the transmitted component of the laser beam. Moreover, the reflected component undergoes dispersion in the delay arm  138  by an extent determined by the properties of the glass block  132 , and the effects of this dispersion will be described later. 
     From the half wave plate  136 , the laser beam proceeds through a further delay arm  140  having a construction analogous to that of arm  138 . The half wave plate  136  is orientated to give desired relative intensities to the orthogonally polarised components produced by polarising beam splitter  144 . Delay arm  140  imposes a delay of T 2  on the component of the laser beam that travels to mirror pair  142  relative to the component that travels straight through polarising beam splitters  144  and  146 . Moreover, the component of the laser beam that travels through glass block  148  undergoes additional dispersion. After the second delay arm  140 , the laser beam travels through a quarter wave plate  150  and then into the chirping unit  12 . 
     The laser  14  emits pulses.  FIGS. 11   a  to  11   h  show the effect of the pulse replicating unit  124  on an arbitrary pulse from the laser  14 . Each of  FIGS. 11   a  to  11   h  provides a pair of graphs of intensity versus time. The upper graph in each pair shows intensity in the polarisation parallel to that of the reflected component produced by polarising beam splitter  128  and the lower graph in each pair shows intensity in the orthogonal polarisation parallel to the transmitted component of polarising beam splitter  128 . The two orthogonal polarisations shown in  FIGS. 11   a  to  11   h  shall henceforth be referred to as the “reference polarisations”. In each of  FIGS. 11   a  to  11   h , the time axes of the upper and lower graphs are aligned to some common zero time. For ease of description, it is further assumed that the polarisations of the transmitted components of polarising beam splitters  128  and  144  are parallel and that the polarisations of the reflected components produced by polarising beam splitters  128  and  144  are parallel. 
       FIG. 11   a  shows the output of the half wave plate  126  in response to an arbitrary pulse from the laser  14 . The half wave plate  126  is positioned to rotate the linear polarisation of the arriving laser pulse so that its intensity is split equally between the reference polarisations giving orthogonally polarised pulses  151  and  153 .  FIG. 11   b  shows the output of polarising beam splitter  128  towards block  132 , i.e. just pulse  151 .  FIG. 11   c  shows the output of polarising beam splitter  128  towards splitter  130 , i.e. just pulse  153 .  FIG. 11   d  shows the output of polarising beam splitter  130 , i.e. pulse  153  and, a time T 1  later, pulse  151 . 
     The light from polarising beam splitter  130  travels towards half wave plate  136 . The half wave plate  136  is angled so as to divide pulse  153  equally between the reference polarisations to create pulses  152  and  154 , as shown in  FIG. 11   e . Likewise, delayed pulse  151  is divided equally into pulses  158  and  156 , again as shown in  FIG. 11   e .  FIG. 11   f  shows the output of polarising beam splitter  144  towards block  148 , i.e. just pulses  154  and  158 .  FIG. 11   g  shows the output of polarising beam splitter  144  towards splitter  146 , i.e. just pulses  152  and  156 .  FIG. 11   h  shows the output of polarising beam splitter  146 , i.e. pulses  152  and  156  and, delayed by a time T 2 , pulses  154  and  158 . The delays T 1  and T 2  are constrained such that all four pulses fall within a pulse repetition period T REP  of the laser  14  (1/T REP  being the rate at which the laser emits pulses). 
     The quarter wave plate  150  converts the linear polarisations of pulses  152  to  158  into circular polarisations so that, when pulses  152  to  158  are applied to a sample, the CARS response that they elicit, when time-averaged, is independent of the specific orientation between the polarisation of the pulses and the structure of the sample. 
     In order to keep  FIGS. 11   a  to  11   h  simple, no attempt has been made to show the dispersive effect of blocks  132  and  148  in those Figures. However,  FIG. 12  shows not only the effect of that dispersion but also the effect of dichroic beam splitter  18  in the chirp unit  12  on the pulses  152  to  158 . Accordingly,  FIG. 12  shows pulse  152  split by the dichroic beam splitter  18  into a Stokes pulse  152   a  and a pump pulse  152   b . Likewise, pulses  154  to  158  are split into respective Stokes pulses  154   a  to  158   a  and respective pump pulses  154   b  to  158   b.    
     Pulse  154  has been dispersed by glass block  148  and therefore “leans forward” in  FIG. 12 , as indicated by the dashed line connecting pulses  154   a  and  154   b . As a result of this dispersion, the onset of the pump pulse  154   b  is delayed slightly with respect to the onset of the Stokes pulse  154   a . This delay alters the size of parameter τ (see  FIG. 5  and the corresponding description) and hence the IFD that pulses  154   a  and  b  would otherwise target according to the current position of adjustable retroreflector  32  and the dispersion introduced by glass blocks  24 ,  28  and  30 . In other words, the delay between the start of Stokes pulse  154   a  and the start of pump pulse  154   b  adjusts the resonant frequency ω v  that pulse  154  targets. 
     Likewise, the start of pump pulse  156   b  is delayed with respect to the start of Stokes pulse  156   a  by the dispersion of glass block  132  and the start of pump pulse  158   b  is delayed with respect to the start of Stokes pulse  158   a  by the dispersion of glass blocks  132  and  148 . Accordingly, all four pulses  152  to  158 , due to their differing degrees of dispersion, target different resonant frequencies in the sample. The chirping of the pulses  152   a  to  158   b  by the glass blocks  24 ,  28  and  30  and the delaying effect of the path difference in the routes to mirrors  26  and  32  is not illustrated in  FIG. 12  in order to avoid complicating the diagram. However, the repetition period T REP  of the pulses from the laser  14  is again shown in  FIG. 12 . 
     As mentioned earlier, the microscope  16  detects CARS pulses from the sample using a photomultiplier which transduces the intensity of the received CARS light into an electrical signal, I(t). Each of  152  to  158  can produce a corresponding pulse of CARS light and these CARS pulses are short compared to the time resolution of this photomultiplier such that the CARS pulses can be considered instantaneous in the electrical signal I(t) Therefore, ignoring noise and the like, the signal I(t) has the form of a series of delta functions that repeats every T REP . The signal I(t) can therefore be expressed as a Fourier series: 
     
       
         
           
             
               I 
               ⁡ 
               
                 ( 
                 t 
                 ) 
               
             
             = 
             
               
                 
                   a 
                   0 
                 
                 2 
               
               + 
               
                 
                   ∑ 
                   
                     i 
                     = 
                     1 
                   
                   ∞ 
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   ( 
                   
                     
                       
                         a 
                         i 
                       
                       ⁢ 
                       cos 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ω 
                         i 
                       
                       ⁢ 
                       t 
                     
                     + 
                     
                       
                         b 
                         i 
                       
                       ⁢ 
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ω 
                         i 
                       
                       ⁢ 
                       t 
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             where 
             ⁢ 
             
               : 
             
           
         
       
       
         
           
             
               ω 
               i 
             
             = 
             
               
                 
                   2 
                   ⁢ 
                   π 
                 
                 
                   T 
                   REP 
                 
               
               ⁢ 
               i 
             
           
         
       
       
         
           
             
               a 
               i 
             
             = 
             
               
                 2 
                 
                   T 
                   REP 
                 
               
               ⁢ 
               
                 
                   ∫ 
                   0 
                   
                     T 
                     REP 
                   
                 
                 ⁢ 
                 
                   
                     I 
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   ⁢ 
                   cos 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ω 
                     i 
                   
                   ⁢ 
                   
                     t 
                     · 
                     
                       ⅆ 
                       t 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               b 
               i 
             
             = 
             
               
                 2 
                 
                   T 
                   REP 
                 
               
               ⁢ 
               
                 
                   ∫ 
                   0 
                   
                     T 
                     REP 
                   
                 
                 ⁢ 
                 
                   
                     I 
                     ⁡ 
                     
                       ( 
                       t 
                       ) 
                     
                   
                   ⁢ 
                   sin 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ω 
                     i 
                   
                   ⁢ 
                   
                     t 
                     · 
                     
                       ⅆ 
                       t 
                     
                   
                 
               
             
           
         
       
     
     The delay arms  138  and  140  are designed such that 2T 1 =4T 2 =T REP . As a result, the set of delta functions that repeats within a period of I(t) of duration T REP  is: 
               I   ⁡     (   t   )       =       ∑     n   =   1     4     ⁢           ⁢       T   REP     ⁢     A   n     ⁢     δ   ⁡     (     t   -         (     n   -   1     )     ⁢     T   REP       4       )                 
where A 1  to A 4  are the time-averaged signals of (the seemingly instantaneous) CARS pulses that are triggered by pulses  152  to  158 , respectively. It can be shown mathematically that:
 
     
       
         
           
             
               
                 a 
                 0 
               
               2 
             
             = 
             
               
                 A 
                 1 
               
               + 
               
                 A 
                 2 
               
               + 
               
                 A 
                 3 
               
               + 
               
                 A 
                 4 
               
             
           
         
       
       
         
           
             
               a 
               1 
             
             = 
             
               
                 A 
                 1 
               
               - 
               
                 A 
                 3 
               
             
           
         
       
       
         
           
             
               b 
               1 
             
             = 
             
               
                 A 
                 2 
               
               - 
               
                 A 
                 4 
               
             
           
         
       
       
         
           
             
               a 
               2 
             
             = 
             
               
                 A 
                 1 
               
               - 
               
                 A 
                 2 
               
               + 
               
                 A 
                 3 
               
               - 
               
                 A 
                 4 
               
             
           
         
       
     
     From these four simultaneous equations, the magnitudes A 1 , A 2 , A 3  and A 4  of the four CARS pulses  152  to  158  can be recovered. 
       FIG. 13  shows an electrical circuit  160  within the microscope  16  for processing the photomultiplier signal I(t) to deduce 
                 a   0     2     ,         
a 1 , b 1  and a 2 . The signal I(t) the photomultiplier is applied on input line  162 . Input line  164  receives an electrical signal that is derived from a photodiode (not shown) within the laser  14  and which consists of a delta function repeated at the pulsing frequency of the laser  14  (limited by the bandwidth of the photodiode which, just to clarify, is typically about 500 MHz, i.e. 8ω 1 ). The electrical signal applied to line  164  is therefore also a Fourier series of the same frequencies that are contained in I(t).
 
     The circuit  160  contains a number of high pass filters  166  to  172 . Filters  166  and  168  block frequencies below 
               ω   1     2         
(it will be recalled that
 
                 ω   1     =       2   ⁢   π       T   REP         )         
and filters  170  and  172  block frequencies below
 
                 3   ⁢     ω   1       2     .         
The circuit  160  also contains a number of low pass filters  174  to  188 . Filters  174  to  180  block frequencies above
 
                 ω   1     2     ,         
filters  182  and  184  block frequencies above
 
               3   ⁢     ω   1       2         
and filters  186  and  188  block frequencies above
 
                 5   ⁢     ω   1       2     .         
The circuit also includes a delay line  190  for delaying the signal exiting filter  182  by
 
               T   REP     4         
to phase shift that signal by
 
             π   2         
radians.
 
     The circuit  160  also includes a number of mixers  192  to  196 , each arranged to perform frequency down conversion. The signals supplied to the circuit  160  contain only frequencies that satisfy the relation kω 1 , where k is an integer (including zero). Therefore, the output of mixer  192  contains a d.c. component that is proportional to a 1 , the output of mixer  194  contains a d.c. component that is proportional to b 1  and the output of mixer  196  contains a d.c. component that is proportional to a 2 . The proportionality constants for a 1 , b 1  and a 2  are determined by the losses of mixers  192  to  196  and by the amplitude of the signal on line  164 . Thus, the CARS system described with respect to  FIGS. 9 to 13  is useful in that various measurements can be time-multiplexed without additional optics. Coefficient a 1  is a measure of the difference in size between CARS pulse heights A 1  and A 2  and can therefore be used in a differential measuring technique, as will now be described. 
     Consider, for example, the CARS pulse that is produced in response to pulse  152 . As explained previously, this CARS pulse will include CARS light from the vibrational mode whose resonant frequency, call it f 0 , is targeted by the IFD to which pulse  152  corresponds. However, the CARS pulse will also include non-resonant CARS light from all the vibrational modes of the material lying within the focal volume of the microscope  16  that have a resonant frequency of greater than f 0 , and also from purely electronic contributions. This non-resonant CARS light is a background CARS signal that tends to mask the wanted CARS signal that is the CARS light from the vibrational mode whose resonant frequency is f 0 . 
     Since water is a dominant component of biological cells, the background CARS signal from water can dominate or mask the resonant CARS signal that is elicited from a vibrational mode of an aspect of a cell that is under investigation. In order to address this problem, the differential nature of coefficient a 1  can be exploited, as follows. 
     Consider that pulse  152 , which, it will be recalled, draws a CARS response of magnitude A 1 , is given by the chirp unit  12  an IFD of f 1  that is the resonant frequency of a vibrational mode of interest within the membrane of a type of cell that is to be studied. Assume also that pulse  154 , which, it will be recalled, draws a CARS response of magnitude A 2 , targets a vibrational mode whose resonant frequency is f 2 &gt;f 1  and is not expected to be found in water or in the type of cell being investigated. 
     First, with the focal volume of the microscope containing only water, the half wave plate  126  is are adjusted to alter the magnitudes of peaks  152  and  156  so that the CARS pulse magnitudes A 1  and A 3  are substantially equal and a 1  (the output signal of filter  176 ) is substantially zero. In this situation, the CARS pulse magnitudes A 1  and A 2  are due entirely to non-resonant CARS light. Then, the sample material is located within the focal volume. Any change that results in the output signal of filter  176  is thus attributable to resonant CARS light from the vibrational mode of interest that has a resonant frequency of f 1 . In other words, the nulling of the output signal of filter  176  by adjusting the half wave plate  126  has the effect of compensating the non-resonant CARS background signal from water when the microscope is used to investigate a real sample. Since all four pulses are derived from the same laser pulse, they do not exhibit equal classical intensity fluctuations, which are completely suppressed in the balanced signal a 1 , which can therefore be limited only by the shot-noise of the signal. This enables a sensitive detection of small changes in material composition. A similar argument holds for the coefficients a 2,3 , so that in total three balanced signals are extracted. 
     With the glass blocks  132  and  148  removed (such that pulses  152  to  158  are all given the same IFD by the chirp unit  12 ), the CARS system  122  can be adapted to perform some other measurements, as will now be explained. 
     The beam directions of the four pulses  152  to  158  can all be made slightly different by the tip/tilt of beam splitters  146  and  130  Then, the microscope will focus the pulses into laterally displaced focal volumes within the sample. Thus, the CARS pulses produced in response to pulses  152  to  158  relate to different locations within the sample. Using a lateral displacement comparable to the size of the focal volume, the coefficient a 1 , represents a spatial gradient in the CARS response within the sample (since A 1  and A 3  now relate to different locations within the sample). Similar arguments hold for a 2,3 . 
     It is also possible to remove the quarter wave plate  150  and replace it with a half wave plate. Under these circumstances, the pulses  152  and  156  emerge from the pulse replicating unit  124  with a first polarisation and pulses  154  and  158  emerge with a second, orthogonal, polarisation. It will be recalled that the CARS pulses elicited by pulses  152  to  158  have magnitudes A 1  to A 4 , respectively. Therefore, coefficient a 2 =A 1 −A 2 +A 3 −A 4  is a measure of the difference of the CARS responses of the sample to first and second polarisations of the pulses  152  to  158 . Thus, it is possible to probe the spatial ordering of the sample material leading to birefringence in the CARS light, as in e.g. in Lipid membranes (see J. Raman Spectrosc. 34, 642-650 (2003)). The additional half wave plate can of course be rotated to rotate the two orthogonal polarisations of the pulses  152  to  158  relative to the sample material. 
     Various modifications of the described CARS systems will be apparent to readers skilled in the art. For example:
         non-polarising beam splitters could be used in the pulse replicating unit  124  (although a loss of intensity would occur when recombining the beams at the output of each of the delay arms  138  and  140 ).   polarising beam splitters  82  and  92  could be omitted with the light from lenses  80  and  90  being focussed on to respective single line scan cameras (although polarisation information about the CARS light would be lost)   a single camera with two lines could be used together with a polarization displacer instead of  82  and  92 .   both outputs of beam splitter  76  could be guided over a single dispersing beam path, using a line scan camera with 2 lines (without polarization displacer) or 4 lines (with polarization displacer)   Prisms  78 ,  88  could be exchanged with gratings   the number of, and disposition of the delayed pulses that the pulse replicating unit  124  manufactures within the laser&#39;s pulse repetition period T REP  could be altered (with concomitant adjustments to circuit  160 ). This can be done without loss of laser power by changing the number of delay units  138 ,  140 . A total number of 2 n  pulses and respective electrical signals are produced for n replica.   the reference beam incident upon beam splitter  76  could be provided directly from laser  14  (depending on the nature of the laser) thus removing the need for non-linear element  62  and lenses  60 , 64 .