Patent Description:
High power lasers are being used increasingly in materials processing applications. Understanding the performance parameters of the laser beam provides important insight into process control and process improvements. Laser beam profilers are used for this purpose. One technique used to measure the quality of a focused laser beam is to acquire multiple images of the Rayleigh scatter of the beam, then process those images digitally to compute parameters such as beam waist size, beam centroid, angular divergence and M<NUM> beam propagation ratio and the like. A laser beam profiler apparatus that measures Rayleigh scattering is described in <CIT> and assigned to Ophir-Spiricon, LLC.

The publication "<NPL>), discloses a laser beam characterization method based on scattered light imaging of a laser beam.

While prior art laser beam profilers have proven useful in the past, some shortcomings have been identified. For instance, the laser beam being measured may not completely overlap the focal planes of the imaging devices of the laser beam profiler. This may produce focal errors that can lead to erroneous beam characterization results. As such, there is an ongoing need for a method and apparatus that detects and compensates for the focal errors.

The present application discloses a method of focus correction of at least one image of a laser beam measurement system in order to accurately compute a wide variety of beam parameters. Exemplary beam parameters include beam waist size and location, beam centroid, Rayleigh range, angular divergence, beam parameter product, and M<NUM> beam propagation ratio. While the description included herewith discusses methods of correcting for focus errors, those skilled in the art will appreciate that a variety of methods may be used to measure and correct for various characteristics of laser beam measurements. Additionally, the focus correction methods described herein may be used with a variety of light beams.

The invention relates to a method defined in claim <NUM>.

Other features and benefits of the method and apparatus for focus correction for multi-image laser beam quality measurements as disclosed will become apparent from a consideration of the following detailed description.

Various illustrations of a method and apparatus for focus correction for multi-image laser beam quality measurements will be explained in more detail by way of the accompanying drawings, wherein:.

Generally, optical systems that are out of focus have a distinct two-dimensional point spread function or transfer function. For small point spread functions where the image changes slowly in one dimension, these functions can be approximated by a set of simpler one-dimensional line spread functions or modulation transfer functions. In the embodiments described below, the two-dimensional point spread function is approximated by simpler one-dimensional line spread functions that may be applied to one slice of an image at a time.

In the embodiments described below, the modulation transfer function for out-of-focus images may be characterized a priori, either mathematically or empirically. This out-of-focus modulation transfer function is denoted G(ξ,d) where ξ represents the spatial frequency and d represents the distance of the object from the focal plane. In the illustrated embodiment, the laser beam quality measurement apparatus may comprise an imaging device and optical system that have a modulation transfer function denoted H(ξ) that may also be characterized a priori by a variety of methods.

In the embodiments described below, images of the beams are deconstructed slice by slice. An approximation of each slice of the image captured by the imaging devices described above may be y(x) = b(x)*g(x,d)*h(x) where x is the pixel location in each slice, y(x) is one slice of the camera image, b(x) is the profile of the beam for that slice, and g(x,d) and h(x) are the spatial domain equivalents of G(ξ,d) and H(ξ) respectively, where the asterisk denotes convolution. To find an estimate of b(x), the distance of the beam from the focal plane for a given slice of the image needs to be determined. That distance, d, can be used to find the composite line spread function by convolving g(x,d) with h(x). When this is done, the resulting function may be used to deconvolve y(x), the given slice of camera image. For digital cameras, y(x) will be discrete, yielding accurate results if y(x) is effectively band limited to spatial frequencies below the Nyquist frequency as described below. In practice, b(x), g(x,d) and h(x) are considered to be discrete as well. An alternate expression of the transfer function needed for deconvolution may be G(ξ,d)H(ξ), which is the Fourier transform of g(x,d)*h(x). This allows the earlier equation to be written equivalently as Y(ξ) = B(ξ)G(ξ,d)H(ξ). In another alternate method, at least one noise term n(x) may be added such that the approximation of each slice may be y(x) = b(x)*g(x,d)*h(x)+n(x) or Y(ξ) = B(k)G(k,d)H(k)+N(k).

Alternatively, the deconvolution can be implemented in two dimensions, which is an approach widely used with focal correction. The two-dimensional point spread function (or impulse responses) h(x,y) and g(x,y,d) may be computed once their one-dimensional modulation transfer functions are known, and they may be used for the two-dimensional deconvolution. Generally, the computing requirements for this approach are significant, and for the purpose of imaging laser beams that do not change rapidly slice to slice, a one-dimensional deconvolution may suffice. Those skilled in the art will appreciate that a number of alternative methods for processing image data may be employed to correct for beam focus errors.

Simply put, the method for focus correction of laser beam quality measurements involves <NUM>) capturing images of the beam and from them determining the axis of the beam in three dimensions, <NUM>) dividing each image into multiple slices, <NUM>) finding the distance from the beam axis to the focal plane for each slice of each image, <NUM>) deconvolving each slice using the transfer function corresponding to that distance, and <NUM>) reassembling the deconvolved slices into an image that can be used to compute beam parameters.

<FIG> shows a laser beam quality measurement apparatus <NUM>. As shown, the apparatus may comprise at least one housing <NUM> with one or more imaging devices <NUM> positioned therein and in optical communication with at least one sampling region <NUM>. One or more optical systems <NUM> may be in optical communication with the sampling region <NUM> and the imaging device <NUM>. Alternatively, the laser beam quality measurement apparatus <NUM> need not include an optical system <NUM>. Further, any number of additional imaging or measurement devices and/or sensors may be used with the laser beam quality measurement apparatus <NUM>. As shown, at least one laser or light source <NUM> may direct at least one beam <NUM> into and/or through the sampling region <NUM>. Those skilled in the art will appreciate that the light source <NUM> may comprise light emitting diodes, superluminescent diodes, flashlight beams and the like. The imaging device <NUM> and optical system <NUM> may be configured to capture one or more light signals from the laser beam <NUM> and direct them via at least one conduit <NUM> to at least one image processing module <NUM>. In one embodiment, the imaging device <NUM> and optical system <NUM> may be configured to capture one or more light signals that are Rayleigh scattered from the beam <NUM>, although those skilled in the art will appreciate that Raman scattering or any variety of scattering effects or other optical phenomena may be observed by the laser beam quality measurement system.

Referring again to <FIG>, the image processing module <NUM> may be configured to process at least one scattered light signal and display one or more images on one or more displays <NUM>. As shown, the beam <NUM> may have one or more focal points or beam waists <NUM> as it propagates through the sampling region <NUM>. In the illustrated embodiment, the beam waist or focal point <NUM> may be defined as the location or region where the beam is most tightly focused or where the cross section of the beam is the smallest or where the beam power or optical fluence is most highly concentrated. In many material processing applications, the user may locate the beam waist on the surface of or within the material to be processed, though those skilled in the art will appreciate that that the beam waist may be positioned at a variety of positions relative to the material to be processed. In one embodiment, the housing <NUM>, the optical system <NUM> and the imaging device <NUM> may define one or more focal planes. In the illustrated embodiment, the housing <NUM>, the optical system <NUM> and the imaging devices <NUM> define two focal planes, Py and Px, and at least one plane Z, although those skilled in the art will appreciate that any number of housings or imaging devices may be used that define any number of planes or focal planes. In the illustrated embodiment, plane Z is substantially orthogonal to the image planes PY and Px, though in another embodiment plane Z may not be orthogonal to the image planes Py and Px. Optionally, the operator may use at least one alignment device <NUM> to align the beam <NUM> within the sampling region <NUM> such that the beam <NUM> substantially intersects both focal planes, Px and Py, although those skilled in the art will appreciate that the use of such an alignment device is not required.

<FIG> and <FIG> show various views of the embodiment of the laser beam quality measurement apparatus <NUM> shown in <FIG>, as looking through plane Z. As shown, one or more light signals <NUM> and <NUM> from the beam <NUM> may be directed to the imaging device <NUM> via the optical system <NUM>. In the illustrated embodiment the light signals <NUM> and <NUM> are Rayleigh-scattered from the beam <NUM>. Those skilled in the art will appreciate that any number of light signals scattered in a variety of ways may be measured. In the illustrated embodiment, the optical system <NUM> and the imaging device <NUM> define focal planes Py and Px oriented orthogonal to each other, although those skilled in the art will appreciate that focal planes Py and Px may not be orthogonal to each other. Optionally, the optical system <NUM> and the imaging device <NUM> may define a single focal plane or more than two focal planes that may intersect at a variety of angles. In short, any number of focal planes may be defined by the optical system <NUM> and/or the imaging device <NUM>. As shown in <FIG>, the beam <NUM> is shown end-on, intersecting the focal planes Py and Px, as though it were entering or exiting the plane Z as the surface of the page. The optical system <NUM> may comprise at least one reflecting surface <NUM> and at least one optical element <NUM>, although those skilled in the art will appreciate that any variety of optical elements and components may be used in the optical system <NUM>. In the illustrated embodiment, the optical system <NUM> comprises two reflecting surfaces <NUM> and <NUM>. In the illustrated embodiment, reflecting surfaces <NUM> and <NUM> are planar mirrors. Optionally, the reflecting surfaces <NUM>, <NUM> may be a dielectric mirrors, replicated mirrors, concave mirrors, convex mirrors, and the like. Also, the reflecting surfaces <NUM>, <NUM> could be a grating, such as echelle gratings, holographic gratings, volume holographic gratings, volume Bragg gratings, and the like. In the illustrated embodiment, the optical element <NUM> is a prism. Optionally, the optical element <NUM> may be a beamsplitter, mirror, or other reflective or refractive optic. Those skilled in the art will appreciate that the optical system <NUM> may comprise any combination of reflecting surfaces, refractive optics, lenses, collimators, filters, spatial filters, irises, stops, and the like. As shown, the scattered light signals <NUM> and <NUM> are reflected by the reflecting surfaces <NUM> and <NUM> respectively and are directed by the optical element <NUM> to the imaging device <NUM>. The imaging device <NUM> may comprise at least one image sensor <NUM> located therein. In the illustrated embodiment, the imaging device <NUM> is a camera with at least one CMOS image sensor <NUM> located therein. Optionally, the image sensor <NUM> may be a charge-coupled device (CCD) image sensor, focal plane array, pyroelectric array, scanning array, time-delay integration imager and the like. Those skilled in the art will appreciate that a wide variety of image sensors, imaging devices or imaging systems may be used with the apparatus <NUM>. Also, those skilled in the art will appreciate that rather than using a single imaging device, multiple imaging devices may be used, or the imaging device <NUM> may be repositionable during use. Also, the scattered light signals <NUM> and <NUM> may be collected by an alternative optical system such as a fiber bundle, an elliptical reflector, or a parabolic reflector that may direct the scattered light signals <NUM>, <NUM> to the imaging device <NUM>. <FIG> described below show various views of alternate embodiments using multiple imaging devices as described herein, wherein similar reference numbers refer to similar components. In the alternative, <FIG> shows an embodiment where a single imaging device is used and the imaging device is repositionable from a first position T<NUM> to a second position T<NUM>, thereby allowing multiple images to be acquired at multiple angles, each image with its own focal plane.

As shown in <FIG>, the imaging device <NUM> may be connected to at least one image processing module <NUM> via at least one conduit <NUM>. Exemplary types of conduits <NUM> include, without limitation, electrical cables (such as USB, FireWire, CATS), fiber optic cables or digital optical cables. Optionally, the conduit <NUM> may comprise network or wireless communication protocols such as GigE Ethernet, Bluetooth, WiFi and the like. The image processing module <NUM> may comprise at least one display <NUM>. Exemplary types of displays <NUM> include, without limitation, computer graphics or graphical user interfaces that are displayed on flat-screen, LED or LCD monitors and the like.

<FIG> show images 134a and 134b relating to the focal planes Py and Px respectively as shown on the display <NUM>. Optionally, the display <NUM> may show a single image or any number of images <NUM>. As shown in <FIG>, in the illustrated embodiment, the beam <NUM> propagates along the intersection of focal planes Py and Px. <FIG> shows at least one image 134a of at least one beam caustic 126a relating to focal plane Py captured by the imaging device <NUM> as the beam <NUM> is aligned so that it propagates through the sampling region <NUM>. The image processing module <NUM> may generate one or more slices of the image 134a by scanning the image 134a with one or more cursors 124a. For example, slices <NUM>, <NUM> and <NUM> may be captured at one or more cursor positions <NUM>, <NUM> and <NUM> respectively. Those skilled in the art will appreciate that any number of slices may be generated by the image processing module <NUM>. The image 134a may exhibit at least one beam waist 128a that is shown approximately in the center of the sampling region <NUM>. Alternatively, the beam waist 128a may be anywhere in the image 134a.

<FIG> of the illustrated embodiment shows at least one image 134b of at least one beam caustic 126b relating to focal plane Px captured by the imaging device <NUM> as the beam propagates through the sampling region <NUM>. In the illustrated embodiment, the image processing module <NUM> may generate one or more slices <NUM>, <NUM> and <NUM> of the beam image 134a by scanning the image 134a with at least one cursor 124a at one or more cursor positions <NUM>, <NUM> and <NUM> respectively. In the illustrated embodiment, the images 134a and 134b shown in <FIG> are substantially identical, exhibiting one or more edges 136a and 136b that may be observed to be in focus, so no focus correction is required. The image processing module <NUM> may use the images 134a, 134b and/or slices <NUM>-<NUM> and <NUM>-<NUM> from <FIG> to compute a set of beam parameters such as beam waist size, location or focal shift, Rayleigh range, beam centroid, angular divergence, beam parameter product and the M<NUM> beam propagation ratio, and the like, that the operator may use to characterize and control performance of the laser or light source <NUM> shown in <FIG>. Those skilled in the art will appreciate that any number of beam parameters or characteristics of the beam <NUM> may be computed.

<FIG> shows a view of an alternate example <NUM> of the beam quality measurement apparatus <NUM> shown in <FIG> and <FIG>. In this example, at least one beam <NUM> may traverse at least one sampling region <NUM> and may be positioned so that it intersects focal plane Py, but not focal plane Px. In the illustrated example, the beam <NUM> includes one or more beam waists <NUM>, though those skilled in the art will appreciate that the beam <NUM> need not include a beam waist <NUM>. If the beam <NUM> is offset from or is not parallel to one or both focal planes, the beam <NUM> may be observed as being out of focus over some or all of its extent. As shown, one or more scattered light signals <NUM> and <NUM> may be directed by at least one optical system <NUM> to one or more image sensors <NUM> positioned in at least one imaging device <NUM>. As described above, many types of image sensors <NUM> may be used in the imaging device <NUM>. In the illustrated example, the optical system <NUM> includes at least one reflecting surface <NUM> and at least one optical element <NUM>, although those skilled in the art will appreciate that any variety of optical elements and components may be used in the optical system <NUM>. In the illustrated example, the optical system <NUM> comprises two reflecting surfaces <NUM> and <NUM>. Alternative components for use in the optical system <NUM> are described above with respect to optical system <NUM>.

<FIG> show images 234a and 234b as captured by the imaging device <NUM>, directed by at least one conduit <NUM> to the image processing module <NUM> and processed by the image processing module <NUM> and shown on the display <NUM>. As shown in <FIG> and <FIG>, the beam <NUM> may intersect the focal plane Py, and the image 234a may be observed to be in focus. <FIG> shows at least one image 234a of at least one beam caustic 226a of the beam <NUM> relating to focal plane Py captured by the imaging device <NUM> as the beam <NUM> propagates through the sampling region <NUM>. In the illustrated embodiment, for example, the image processing module <NUM> may generate one or more slices <NUM>, <NUM> and <NUM> by scanning the image 234a with at least one cursor 224a at cursor positions <NUM>, <NUM> and <NUM> respectively. Those skilled in the art will appreciate that any number of slices may be generated by the image processing module <NUM>. In the illustrated embodiment, the image processing module <NUM> may be configured to analyze the image to determine at least one axis B<NUM> and to use that data to compute the distance d from a point on B<NUM> corresponding to each slice to the focal plane Px, whose position is known. For example, once the axis B<NUM> is defined, the distance d from the center of slice <NUM> to the focal plane Px is computed and denoted d<NUM>. The image processing module <NUM> then uses the location of axis B<NUM> at each slice, assigning the values of the distances d<NUM>, d<NUM> and d<NUM> from each respective slice. As described below, this distance data is used to deconvolve each slice using the transfer function corresponding to that distance, and reassemble the deconvolved slices into an image that can be used to compute the correct beam parameters of the beam <NUM>.

Referring to <FIG> and <FIG> of the illustrated embodiment, the display <NUM> of the image processing module <NUM> shows at least one image 234b of the beam caustic 226a of the beam <NUM> relating to focal plane Px, captured by the imaging device <NUM> as the beam <NUM> propagates through the sampling region <NUM>. As shown in <FIG>, the image processing module <NUM> may generate slices <NUM>, <NUM> and <NUM> of the beam image 234b with at least one cursor 224b at cursor positions <NUM>, <NUM> and <NUM> respectively. In the illustrated embodiment, because the beam <NUM> is offset from focal plane Px, the image 234b and slices <NUM>, <NUM> and <NUM> may be observed as being out of focus, causing the image 234b to appear blurry. Also, the image of the beam waist 228b captured in slice <NUM> at cursor position <NUM> may appear smaller or larger than it should be. The blurry appearance of the image 234b may cause the laser beam quality measurement system to yield incorrect beam parameter results. However, the image processing module <NUM> may be configured to correct for the blur of the image 234b by using the distances d<NUM>, d<NUM>, d<NUM>, etc. calculated from the image 234a to determine at least one out-of-focus transfer function G(ξ,d) for each slice, which is used in combination with the known modulation transfer function H(ξ) of the system to deconvolve each slice. The images formed by reassembling the deconvolved slices can then be analyzed to compute the correct beam parameters described above. Those skilled in the art will appreciate that any combination of beam measurements or processing algorithms may be used to correct the focus errors caused by the axis of the beam <NUM> not being coincident with the focal planes of the apparatus <NUM>.

<FIG> and <FIG> show various images of alternate view <NUM> of the beam quality measurement apparatus shown in <FIG> and <FIG> where at least one beam <NUM> traverses at least one sampling region <NUM> and is positioned such that it intersects but may not be parallel to at least one of focal planes Py and Px. In the illustrated embodiment, the beam <NUM> may include one or more beam waists <NUM>, though those skilled in the art will appreciate that the beam <NUM> need not have a beam waist <NUM>. As shown in <FIG>, one or more scattered light signals <NUM> and <NUM> scattered from the beam <NUM> may be directed by at least one optical system <NUM> to one or more image sensors <NUM> positioned in at least one imaging device <NUM>. As described above, many types of image sensors <NUM> may be used in the imaging device <NUM>. In the illustrated embodiment, the optical system <NUM> includes at least one reflecting surface <NUM> and at least one optical element <NUM>, although those skilled in the art will appreciate that any variety of optical elements and components may be used in the optical system <NUM>. In the illustrated embodiment, the optical system <NUM> comprises two reflecting surfaces <NUM> and <NUM>. Alternative components for use in the optical system <NUM> are described above with respect to optical system <NUM>. <FIG> shows at least one image 334a of at least one beam caustic 326a of the beam <NUM> relating to focal plane Py, as captured by the image sensor <NUM> of the imaging device <NUM> (shown in <FIG>) as the beam <NUM> propagates through the sampling region <NUM> and is directed by at least one conduit <NUM> to at least one image processing module <NUM>. In the illustrated embodiment, the image processing module <NUM> may generate slices <NUM>, <NUM> and <NUM> by scanning the image 334a with at least one cursor 324a at cursor positions <NUM>, <NUM> and <NUM> respectively. In the illustrated embodiment, the image processing module <NUM> may analyze the image to define an axis C<NUM> that is shown as slanted at angle β relative to the focal plane Px, but the image 334a otherwise may be observed to be in focus. <FIG> shows an image 334b of at least one beam caustic 326b of the beam <NUM> relating to focal plane Px, captured by the imaging device <NUM> and processed by the image processing module <NUM>. The image processing module <NUM> may generate slices <NUM>, <NUM>, <NUM> by scanning the image 334b with at least one cursor 324b at locations <NUM>, <NUM> and <NUM> respectively. In the illustrated embodiment, because the beam <NUM> may intersect focal plane Px only at the beam waist 328b, only the beam waist 328b may be observed to be in focus, and the remainder of the image 334b may be observed to be out of focus. Those skilled in the art will appreciate that the beam <NUM> may intersect focal planes Py and Px at a variety of angles, or the beam <NUM> may intersect neither focal plane Py and Px.

<FIG> show various views of image 334a of the beam <NUM> as shown on the display <NUM>. In the illustrated embodiment, <FIG> shows the image 334a as shown in <FIG>, with slices <NUM>-<NUM> generated by the image processing module <NUM> by scanning the image 334a with cursor 324a at cursor positions <NUM>-<NUM>. Those skilled in the art will appreciate that many more slices may be created and analyzed by the image processing module <NUM> to provide increased resolution. As shown in <FIG>, the image processing module <NUM> analyzes the image 334a to define the optical axis C<NUM>. Optionally, the image processing module <NUM> may analyze multiple images to define any number of optical axes. For example, in the illustrated embodiment, once the optical axis C<NUM> is defined, distances d<NUM> through dass from the optical axis C<NUM> to the image plane Px (whose position is known) may be calculated for each slice <NUM>-<NUM> by the image processing module <NUM>. As described below, this data may then be used to remove the out-of-focus blur of the image 334b shown in <FIG> and <FIG>. Those skilled in the art will appreciate that the out of focus blur may be corrected by applying a variety of optical or signal processing methods to the images of the beam <NUM>.

<FIG>, <FIG> and <FIG> show the progression of image 334b shown in <FIG> from being out of focus to being in focus, as displayed on the display <NUM>. <FIG> shows an image 334b of the beam caustic 326b as captured by the imaging device <NUM> and processed by the image processing module <NUM>. The image processing module <NUM> may generate slices <NUM>-<NUM> by scanning the image 334b with at least one cursor 324b at locations <NUM>-<NUM>. Those skilled in the art will appreciate that the image processing module <NUM> may capture any number of slices at any number of positions along the sampling region <NUM>. Because the beam <NUM> is not parallel to the focal plane Px, one or more of the slices <NUM>-<NUM> may appear out of focus. In this embodiment, because the beam waist 328b at cursor position <NUM> intersects the focal plane, the beam waist 328b may be observed to be in focus, though those skilled in the art will appreciate that the beam waist 328b may not be in focus, and a different location of the beam may be in focus instead. In contrast to the slice <NUM> at the beam waist, for example, slices <NUM>-<NUM> and <NUM>-<NUM> may become progressively more out-of-focus the further they are from the beam waist position <NUM>. The distances d<NUM> through dass from the center of slices <NUM>-<NUM> to the optical axis C<NUM> as shown in <FIG> as described above are used to deconvolve each slice <NUM>-<NUM> using the in-focus transfer function H(ξ) and the out-of-focus transfer function G(ξ,d) corresponding to that distance, and reassemble the deconvolved slices into an image 334c shown in <FIG> with slices <NUM>-<NUM> that can be used to compute the correct beam parameters such as beam divergence and beam propagation ratio M<NUM> as described above.

<FIG> show views of an alternate beam quality measurement apparatus <NUM> configured with multiple imaging devices. As shown in <FIG> and <FIG>, the laser beam quality measurement apparatus <NUM> may comprise at least two imaging devices <NUM> and <NUM> that may be in optical communication with at least one beam <NUM> propagating through at least one sampling region <NUM>. The imaging devices <NUM> and <NUM> may be configured to capture one or more light signals <NUM> and <NUM> scattered from the beam <NUM> and direct them via at least two conduits <NUM> and <NUM>, respectively, to at least one image processing module <NUM>. Those skilled in the art will appreciate that a single conduit may be used. Exemplary types of conduits <NUM> include, without limitation, electrical cables (such as USB, FireWire, CATS), fiber optic cables or digital optical cables. Optionally, the conduit <NUM> may comprise network or wireless communication protocols such as GigE Ethernet, Bluetooth, WiFi and the like. The imaging processing module <NUM> may be configured to process the signals <NUM> and <NUM> and display one or more beam images <NUM> on one or more displays <NUM>. The imaging devices <NUM> and <NUM> may further comprise at least one image sensor <NUM> and <NUM>, respectively. In the illustrated embodiment, the imaging devices <NUM> and <NUM> are cameras with at least one CMOS image sensors <NUM>, <NUM> disposed therein. Optionally, the image sensors <NUM>, <NUM> may comprise charge-coupled device (CCD) image sensors, focal plane arrays, pyroelectric arrays, scanning arrays, time-delay integration imagers and the like. Those skilled in the art will appreciate that a wide variety of imaging sensors, imaging devices or imaging systems may be used with the apparatus <NUM>. As shown in <FIG>, the imaging devices <NUM> and <NUM> are separated by at least one angle α. In the illustrated embodiment, angle α may be <NUM>°, making the imaging devices orthogonal to each other in at least one plane. Alternatively, angle α may be anywhere between <NUM> and <NUM> degrees. As described above, the image processing module <NUM> may analyze the images <NUM> shown in the display <NUM> to compute various beam parameters.

<FIG> shows an alternate view of the laser beam quality measurement apparatus <NUM> shown in <FIG>. In the illustrated example, the imaging devices <NUM> and <NUM> may define focal planes Py and Px, respectively, oriented orthogonal to each other, although those skilled in the art will appreciate that focal planes Py and Px may not be orthogonal to each other. Optionally, the imaging devices <NUM> and <NUM> may define a single focal plane or more than two focal planes that may intersect at a variety of angles. As shown in <FIG>, the beam <NUM> is shown end-on, intersecting the focal planes Py and Px, as though it were entering or exiting the surface of the page. As shown in <FIG> and <FIG>, in the illustrated embodiment, the beam <NUM> propagates along the intersection of focal planes Py and Px. The display <NUM> shows images 434a and 434b relating to the focal planes Py and Px, respectively, as captured by imaging devices <NUM> and <NUM> respectively. Optionally, the display <NUM> may show a single image or any number of images <NUM>. In the illustrated embodiment, the images 434a and 434b displayed on display device <NUM> are substantially similar and may be observed to be in focus. In this embodiment, because both images 434a and 434b are in focus, no focus correction is required. The image processing module <NUM> may use the images 434a and 434b to compute a set of beam parameters such as beam waist size, location or focal shift, Rayleigh range, beam centroid, angular divergence, beam parameter product and the M<NUM> beam propagation ratio, and the like, that the operator may use to characterize and control performance of the laser or light source <NUM> shown in <FIG>. Those skilled in the art will appreciate that any number of beam parameters or characteristics of the beam <NUM> may be computed.

<FIG> shows an alternate view of the laser beam quality measurement apparatus <NUM> shown in <FIG>. As shown, the beam <NUM> may traverse at least one sampling region <NUM> and may be positioned so that it intersects focal plane Py, but not focal plane Px. If the beam <NUM> is offset from or is not parallel to one or both focal planes, the beam <NUM> may be observed as being out of focus over some or all of its extent. In the illustrated embodiment, display <NUM> shows images 444a and 444b as captured by the imaging devices <NUM> and <NUM>, respectively, and processed by the image processing module <NUM>. As shown in <FIG>, because the beam <NUM> intersects the focal plane Py, the image 444a may be observed to be in focus. In contrast, because the beam <NUM> does not intersect focal plane Px, the image 444b may be observed to be out of focus. The method of correction of the image 444b may be similar to that applied to image 234b shown above in <FIG>, <FIG>. In the illustrated embodiment, for example, the image processing module <NUM> may generate one or more slices <NUM>, <NUM> and <NUM> by scanning the image 444a with at least one cursor 424a various positions along the image 444a. Those skilled in the art will appreciate that any number of slices may be generated by the image processing module <NUM>. In the illustrated embodiment, the image processing module <NUM> may be configured to analyze images 444a and 444b to determine at least one axis B<NUM> and to use that data to compute the distance d from the center of each slice <NUM>-<NUM> to the focal plane Px, whose position is known. The image processing module <NUM> may also be configured to determine the distance d from the center of each slice <NUM>-<NUM> to the focal plane Py. The values of the distances d<NUM>, d<NUM> and d<NUM> from the center of their respective slices to the axis Px is used to deconvolve each slice using the transfer function corresponding to that distance, and reassemble the deconvolved slices into a corrected image relating to focal plane Px that can be used to compute the correct beam parameters of the beam <NUM>.

<FIG> shows an alternate view of the laser beam quality measurement apparatus <NUM> shown in <FIG>. As shown, similar to <FIG> above, the beam <NUM> traverses at least one sampling region <NUM> and is positioned such that it intersects but may not be parallel to at least one of focal planes Py and Px. In the illustrated embodiment, display <NUM> shows images 454a (relating to focal plane Py) and 454b (relating to focal plane Px) as captured by the imaging devices <NUM> and <NUM>, respectively, and processed by the image processing module <NUM>. As shown in the display <NUM>, the image 454a appears slanted at an angle relative to focal plane Px but otherwise may be observed to be in focus. Image 454b appears to be focused only at the beam waist 428b. The method of correction of the image 454b may be similar to that applied to image 334b shown above in <FIG>, <FIG>, <FIG> and 9A-9C. In the embodiment shown in <FIG>, the image processing module <NUM> may generate slices <NUM>-<NUM> by scanning the image 454a with cursor 455a. The image processing module <NUM> may analyze the image to define an axis C<NUM>. Optionally, the image processing module <NUM> may analyze any number of images to define any number of optical axes. The image processing module <NUM> may generate slices <NUM>-<NUM> by scanning the image 454b with cursor 455b. Those skilled in the art will appreciate that the beam <NUM> may intersect focal planes Py and Px at a variety of angles, or the beam <NUM> may intersect neither focal plane Py and Px. As described similarly above with respect to <FIG>, <FIG>, <FIG> and <FIG>, the image processing module <NUM> may compute the distances d<NUM> through d<NUM> from the center of slices <NUM>-<NUM> to the optical axis C<NUM> and use them to deconvolve each slice <NUM>-<NUM> using the in-focus transfer function H(ξ) and the out-of-focus transfer function G(ξ,d) corresponding to each distance, and reassemble the deconvolved slices into an image 454c shown in <FIG> that can be used to compute the correct beam parameters such as beam divergence and beam propagation ratio M<NUM> as described above. Those skilled in the art will appreciate that the out of focus blur may be corrected by applying a variety of optical or signal processing methods to the images of beam <NUM>.

Claim 1:
A method comprising:
providing at least one imaging device (<NUM>) defining at least one first focal plane (Py) and at least one second focal plane (Px), the at least one imaging device (<NUM>) including at least one image sensor (<NUM>) configured to capture one or more images of one or more scattered light signals (<NUM>, <NUM>) scattered through Rayleigh scattering from at least one laser beam (<NUM>) propagating through at least one sampling region (<NUM>), wherein the at least one imaging device (<NUM>) includes at least one in-focus modulation transfer function H(ξ);
providing at least one image processing module (<NUM>) having at least one display (<NUM>)
capturing at least one in-focus image (234a) in the first focal plane (Py) of a first scattered light signal (<NUM>) and at least one out-of-focus image (234b) in the second focal plane (Px) of a second scattered light signal (<NUM>) with the at least one image sensor (<NUM>);
generating one or more slices (<NUM>, <NUM>, <NUM>) of the scattered laser beam signals by scanning the at least one in-focus image (234a) with at least one cursor (224a) at one or more cursor positions (<NUM>, <NUM>, <NUM>);
determining at least one first axis (B<NUM>) of the at least one in-focus image (234a) in the at least one first focal plane (Py) with the at least one image processing module (<NUM>);
computing a distance, d, from a center of each of the slices (<NUM>, <NUM>, <NUM>) to the second focal plane (Px), the center of a slice being the point on the first axis (B1) corresponding to the slice, and assigning values of the distances (d<NUM>, d<NUM>, d<NUM>) from each respective slice (<NUM>, <NUM>, <NUM>), wherein the center of each of the slices (<NUM>, <NUM>, <NUM>) is defined relative to the at least one in-focus image 234a;
determining at least one out-of-focus transfer function G(ξ,d) for each of the slices (<NUM>, <NUM>, <NUM>) in the out-of-focus image (234b) using the assigned values of the distances (d<NUM>, d<NUM>, d<NUM>);
deconvolving each slice (<NUM>, <NUM>, <NUM>) of the out-of-focus image (234b) against the in-focus modulation transfer function H(ξ) and the at least one out-of-focus transfer function G(ξ,d); and
outputting at least one corrected image to the at least one display (<NUM>), and
using the at least one corrected image to calculate a width of at least one beam waist shown in the corrected image.