Patent Grant
7115848
The present invention relates generally to microscopy imaging apparatus and an imaging method for generating an image which generally contains only in-focus detail, and more specifically to calibration techniques for same.
With a conventional light microscope three-dimensional structures typically cannot be successfully imaged. Ordinarily, the resultant image consists of a sharp image of an in-focus region of a three-dimensional structure as well as defocused images of the structures above and below the in-focus region. A conventional light microscope is unable to reject out-of-focus detail.
Confocal microscopes have been developed which optically section a three-dimensional structure to provide in-focus images of individual layers or strata of the structure. These individual layers can be subsequently combined to form an in-focus three-dimensional image of the complete volume structure. Unfortunately, the light budget of confocal microscopes is generally poor when incoherent light sources are used. Laser scanning confocal microscopes can achieve a very shallow depth of focus, but typically require expensive apparatus and an illuminating/imaging pinhole through which the laser light is focused.
In U.S. Pat. No. 5,381,236 to Morgan, an optical sensor is described which is used to determine the range (distance) of individual features of a three-dimensional structure. The sensor has a periodic patterned light source that illuminates the structure and is reversible (i.e. the pattern is phase shifted 180°). An array of detector elements aligned to the pattern of the light source is used to detect an image of the pattern and the reversal of the pattern illuminating the structure. As the pattern is generally only imaged well on those parts of the structure which are themselves in focus, this enables the range (distance) of in-focus parts of the structure to be determined. A potential shortcoming of the apparatus and method described in Morgan can be that, in order to operate properly, the individual elements of the detector should be exactly aligned with and matched to the pattern of the light source. In practice this has been found to be almost impossible to achieve.
One solution to the problem is offered in U.S. Pat. No. 6,376,818 to Wilson et al., the disclosure of which is incorporated herein by reference in its entirety. The technique discussed in Wilson et al. involves the superposition of a periodic pattern of transparent and non-transparent stripes onto the object of interest. At least three images are recorded at different spatial phases of the pattern by means of a microscope with a shallow focal depth. A three-dimensional image composed of only in-focus detail is then derived from the recorded images (this technique is known in some circles as a “full-focus” technique). An exemplary system of this variety is the OPTIGRID™ microscopy system, available from Thales Optem, Fairport, N.Y.
Unfortunately, conventional microscopy imaging masks utilized, for example, by Wilson et al. can leave residual patterning in the final image. The degree of the residual pattern is a function of the intensity profile in the illumination pattern. Such residual patterning is undesirable since it raises doubt as to whether the pattern is part of the specimen or an artifact of the imaging process.
Because of the accessibility and easy fabrication, ronchi gratings (i.e., square waves) have been used in structured illumination. However, when imaged through band-limited systems (such as an optical system) the resultant image has residual patterns. This occurs because the ronchi grating passed through a linear band-limited system is the convolution of the ronchi grating and the point spread function (PSF) of the optics. The result is a square wave with rounded shoulders. It is at these shoulders where residual lines occur. For this reason, it is desirable with some systems to utilize “stripes” in the illumination pattern that vary sinusoidally in intensity.
One issue that can arise with full-focus techniques, and particularly those that utilize a set of sinusoidally-varying stripes in the pattern, is related to the calibration of the system. Generally speaking, microscopy errors can occur if the system is not precisely calibrated. In particular, it can be important to calibrate the location of a mask or similar device that produces the pattern of stripes, particularly as the mask is positioned for different phases. It would be desirable to improve performance of full-focus systems via new calibration techniques.
As a first aspect, embodiments of the present invention are directed to a method of calibrating an imaging system. The imaging system on which the method is practiced includes: a light source; a substrate for supporting an object; a patterning mask that generates a substantially periodic spatial pattern on the object; a phase shifter that adjusts the relative position of the patterning mask and object to shift the position of the pattern on the object; a detector that detects images of the object; and an analyzer that analyzes at least three images of the object, each of which represents a different spatial shift of the pattern, the analyzer being configured to remove the spatial pattern from the images to generate an optically sectioned image of the object. The method comprises: calibrating the position of the mask relative to the substrate via a phase-voltage technique; calibrating the position of the mask relative to the substrate via a merit function technique; and operating the calibrated imaging system.
As a second aspect, embodiments of the present invention are also directed to a method of calibrating an imaging system using a phase-voltage technique. In these embodiments, the imaging system includes: a light source; a substrate for supporting an object; a patterning mask that generates a substantially periodic spatial pattern on the object; a phase shifter that adjusts the position of the patterning mask to shift the position of the pattern on the object, the phase shifter including a piezoelectric device that adjusts the position of the mask responsive to an applied voltage; a detector that detects images of the object; and an analyzer that analyzes at least three images of the object, each of which represents a different spatial shift of the pattern, the analyzer being configured to remove the spatial pattern from the images to generate an optically sectioned image of the object. The method comprises the steps of: (a) generating Fourier Transform data for the phase and voltage of the system; (b) collecting phase data from the system; (c) calculating the phase for each data point of the phase data; (d) unwrapping the phase data to eliminate any 2π discontinuities therein; (e) determining whether each of the unwrapped data points are valid data points to eliminate data points that represent amplifier saturation; (f) identifying phase 1 and phase 2 data points that are nearest calculated values; and (g) interpolating between phase 1 and phase 2 data points identified in step (f) to establish phase 1 and phase 2 voltages.
As a third aspect, embodiments of the present invention are directed to a method of calibrating an imaging system using a merit function technique. In these embodiments, the imaging system includes: a light source; a substrate for supporting an object; a patterning mask that generates a substantially periodic spatial pattern on the object; a phase shifter that adjusts the relative position of the patterning mask and object to shift the position of the pattern on the object; a detector that detects images of the object; and an analyzer that analyzes at least three images of the object, each of which represents a different spatial shift of the pattern, the analyzer being configured to remove the spatial pattern from the images to generate an optically sectioned image of the object. The method comprises the steps of: (a) providing initial phase and voltage values for phases 1, 2 and 3; (b) normalizing one intensity frame; (c) processing a trio of intensity frames; (d) using the trio of frames from step (c), calculating the second harmonic of the resultant image and resulting merit function; (e) performing an inquiry regarding whether the merit function result is below a predetermined threshold value; (f) if step (e) provides a negative result, determining new phase and voltage step sizes; (g) calculating differential phase values with the data from step (f); (h) calculating derivative voltage values with the results from step (g); (i) obtaining imaging system data for a phase 1 derivative; (j) obtaining imaging system data for a phase 2 derivative; (k) calculating gradient differences and correction factors with the data from steps (g)–(j); (l) calculating new values of phases and voltages; and (m) repeating steps (a)–(l) until the merit function result is below the predetermined threshold value recited in step (e).
As a fourth aspect, embodiments of the present invention are directed to imaging systems. These systems comprise: a light source; a substrate for supporting an object; a patterning mask that generates a substantially periodic spatial pattern on the object; a phase shifter that adjusts the relative position of the patterning mask and object to shift the position of the pattern on the object; a detector that detects images of the object; and an analyzer that analyzes at least three images of the object, each of which represents a different spatial shift of the pattern, the analyzer being configured to remove the spatial pattern from the images to generate an optically sectioned image of the object. The system further comprises: means for calibrating the position of the mask relative to the substrate via a phase-voltage technique; and means for calibrating the position of the mask relative to the substrate via a merit function technique.
As a fifth aspect, embodiments of the present invention are directed to computer program products for calibrating an imaging system. The imaging system includes: a light source; a substrate for supporting an object; a patterning mask that generates a substantially periodic spatial pattern on the object; a phase shifter that adjusts the relative position of the patterning mask and object to shift the position of the pattern on the object; a detector that detects images of the object; and an analyzer that analyzes at least three images of the object, each of which represents a different spatial shift of the pattern, the analyzer being configured to remove the spatial pattern from the images to generate an optically sectioned image of the object. The computer program product comprises a computer usable storage medium having computer readable program code embodied in the medium, the computer readable program code comprising: computer readable program code that calibrates the imaging system using a phase-voltage technique; and computer readable program code that calibrates the imaging system using a merit function technique.
The present invention will now be described more fully hereinafter, in which preferred embodiments of the invention are shown. This invention may, however, be embodied in different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. In the drawings, like numbers refer to like elements throughout. Thicknesses and dimensions of some components may be exaggerated for clarity.
Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the description of the invention and the appended claims, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items.
Basic Structure and Operation of the Imaging Apparatus
The imaging apparatus 8 shown in
Referring again to
In the embodiment of the apparatus 8 illustrated in
Referring still to
Ip=√{square root over ((I1−I2)2+(I1−I3)2+(I2−I3)2)}{square root over ((I1−I2)2+(I1−I3)2+(I2−I3)2)}{square root over ((I1−I2)2+(I1−I3)2+(I2−I3)2)}
Implementing this procedure for each pixel of the image is, however, computationally intensive. Alternatively, to enable real-time imaging to be performed without the need for dedicated image processing apparatus, the analyzer 16 may include a look-up table connected to the pattern removal module 18. The look-up table is a tabulation of all possible solutions to the above equation with respect to the three input image values and enables the image I to be determined by reference to the table rather than through calculation of the solution of the equation for each pixel.
The imaging apparatus 8 described above takes advantage of the fact that any non-zero spatial frequency in the image of the object attenuates as the apparatus 8 is defocused. This means that the mask pattern can only be imaged well on those parts of the object O that are in focus and, thus, can provide a means of sectioning those parts of the object O that are in focus, albeit with an undesirable fringe pattern superimposed. By recording three or more images of the object at the same focal position but with different superimposed spatial phases of the pattern, it is possible for the images to be analyzed to remove the superimposed patterns to reveal an optically sectioned image of the object O.
In some embodiments, the mask 14 is in the form of a linear grating that varies sinusoidally in intensity. Alternating transparent and non-transparent bands of equal width are also suitable. A pattern of wider bands results in a thicker er optical section. Typical band widths include bands of 5–30 microns, 12½ microns in particular, though different widths will be appropriate according to the optical sectioning desired. However, any applied substantially periodic light intensity pattern may be employed. Suitable alternative masks include a spiral grating or pie-chart grating. Moreover, two-dimensional periodic patterns may also be used, such as a checkerboard pattern. An exemplary mask is described in co-assigned and co-pending U.S. patent application Ser. No. 10/953,140; filed concurrently, entitled “Illumination Masks that Produce Light Intensity Patterns Substantially Free of Harmonic Distortion”.
As the pattern spacing determines the depth of the optical sectioning, it may be desirable that the pattern spacing (spatial periodicity) of the mask 14 is selected and the illumination magnification is arranged so that only the fundamental of the pattern is projected onto the object O. In the case of the linear square wave grating described above, in which the three phases of the grating Φ, Φ+120° and Φ+240° are projected onto the object O, the third harmonic is automatically cancelled out in the subsequent processing of the three images and so it is not essential to avoid the third harmonic being projected on to the object O. This can provide greater freedom in the overall design of the imaging apparatus 8. In general, when the difference between the n phase shifts of the pattern projected onto the object O is the same in each case the nth harmonic and harmonics thereof are automatically cancelled out.
The imaging apparatus 8 described above employs three or more discrete predetermined phase shifts of the pattern that are projected onto the object O. Where the spatial phase of the pattern is varied continuously, for example using a rotating spiral mask or continuous movement of a grid-type mask, the images of the object O may be integrated over predetermined time periods to generate the optically sectioned image.
A specific embodiment of an optical system of the present invention is illustrated in
I(t,w)=∫∫S(t0,w0|∫∫h1(t0+t1,w0+w1)τ(t1,w1)h2(t1+t,w1+w)dt1dw1|2dt0dw0 (1)
where h1,2 represents the amplitude point spread functions of the two lenses. Optical co-ordinates (t,w) can be related to real co-ordinates (x,y) via
where n sin α is the numerical aperture (NA) and λ denotes the wavelength. The illumination mask can be assumed to take the form of a one-dimensional grid, which for simplicity may be expressed as:
S(t0,w0)=1+m cos(νt0+φ0) (2)
where m denotes a modulation depth and ΦO an arbitrary spatial phase. The normalised spatial frequency ν is related to the actually spatial frequency ν via ν=βλν/NA, where β denotes the magnification between the grid plane and the specimen plane. Substituting equation (2) into equation (1) gives:
I(t,w)=I0+Ic cos φ0+Is sin φ0 (3)
where IO is given by equation (1) with S=1 and, of course, represents a conventional wide field image. Ic and Is represent the image due to masks of the form m cos(νt0) and m sin(νt0) respectively. If Ip=(IC2+IS2)1/2, the grid pattern can be removed from the image of the specimen. This is achieved by taking three images, I1, I2 and I3 corresponding to the relative spatial phases Φ0=0, Φ0=2π/3 and Φ0=4π/3 respectively. Thus obtained is an optically sectioned image, which does not contain IO, by calculating
Ip=√{square root over ((I1−I2)2+(I1−I3)2+(I2−I3)}{square root over ((I1−I2)2+(I1−I3)2+(I2−I3)}{square root over ((I1−I2)2+(I1−I3)2+(I2−I3)})2
The technique is analogous to square law detection in communications systems, and can be described also as grouping the recorded images into pairs of images and calculating the square root of the sum of the squares of the differences between the recorded images in each pair of images. Use of this technique is described in detail in Wilson et al., supra, and need not be described in further detail herein.
Calibration Techniques
Calibration of an imaging apparatus as described above can be very important to successful operation. In particular, it can be quite important that the location of the mask that imparts the grid on the object to be imaged, and in turn the location of the grid itself, is accurate, as only a small deviation from the intended phase can skew results. This can be especially true if a sine wave-type intensity gradient is employed in the creation of the grid. Under ideal conditions, a series of sine waves separated equally in phase over one period of the wave should, when summed, combine to form a straight line. However, if harmonics are introduced into the sine waves of the series, these can create disturbances in the sine waves such that the resultant sum is also a sine wave. As an example of this behavior,
The presence of 2nd, 4th and other harmonics in the grid pattern in the imaging system manifests itself in the appearance of 3rd order residual lines in the processed image. Residual lines result in misinformation in the processed image. Also, when a grid is not positioned accurately, then a second harmonic residual pattern appears on the processed image. The magnitude of residual lines can be 1.65%/degree of phase error. Thus, by positioning the grid accurately, the 2nd harmonic content can similarly be reduced and/or minimized.
In some embodiments of the invention, the imaging system may be calibrated with a dual calibration method. Such a method is illustrated in
Phase Calibration
One technique for calibrating an imaging apparatus of the present invention is to perform a phase-voltage calibration. This technique comprises mapping the measured voltage of a piezoelectric device acting as the phase shifter of the mask and mapping the corresponding position of the phase of the grid. This technique is completely analytic (particularly when employing a Fourier Transform of the magnitude and phase intensity) and can converge quickly to a solution if the Φ, Φ+120′, and Φ+240° phase conditions minimizes the residual lines.
Generally speaking, and with reference to
In this technique, certain parameters may be watched closely. For example, the phase should be monitored for both phase-unwrapping and for voltage saturation effects. As noted above, the phase of the grid is subject to a 2π phase discontinuity. If such a discontinuity is found, the data should be redistributed to allow a smooth representation thereof. This can be accomplished, for example, looking for a 2π phase jump, then removing it by adding or subtracting 2π to all subsequent data points. The result is an unwrapped phase plot (see
The data may also be manipulated to eliminate a region at the large drive voltage end where the amplifier has been saturated and no further voltage increase accompanies increasing drive counts. The result is a flattening of the phase vs. voltage curve (see
Once the data set is deemed to be acceptable (e.g., the 2π discontinuity and the voltage saturation effects have been eliminated), the data can be analyzed with a curve-fitting technique to interpolate values along the phase and voltage curve (see, e.g.,
Merit Function Calibration
Another technique for calibrating an imaging system of the present invention is a merit-function optimization technique. Because the second harmonic residual lines are generally undesirable, and because it has been determined that calibration error is a predominant, if not the only, source of second harmonic residual lines, a technique that seeks to minimize the impact of second harmonic residual lines should be effective in calibrating the imaging system.
If it is assumed that calibration error is the sole source for producing second harmonic residual lines, the second harmonic content of the residual lines can be a metric function for calibration. As such, a damped optimization routine based on this merit function can be employed.
For example, if a 3 phase system is in place (e.g., Φ, Φ+120°, and Φ+240°), one of these phase steps can be employed as a reference, with the other two phase steps being variables. Using this as a basis, a map of the second harmonic can be plotted (see, e.g.,
As an example, if the initial starting values of phase positions 2 and 3 are within ±25 degrees of 120 and 240 degrees, the merit function remains essentially a sloped cone (see
Computer Program Product for Calibration
The present invention may be embodied in hardware and/or in software (including firmware, resident software, micro-code, etc.). Furthermore, the present invention may take the form of a computer program product on a computer-usable or computer-readable storage medium having computer-usable or computer-readable program code embodied in the medium for use by or in connection with an instruction execution system. In the context of this document, a computer-usable or computer-readable medium may be any medium that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
The computer-usable or computer-readable medium may be, for example but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, device, or propagation medium. More specific examples (a nonexhaustive list) of the computer-readable medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, and a portable compact disc read-only memory (CD-ROM). Note that the computer-usable or computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via, for instance, optical scanning of the paper or other medium, then compiled, interpreted, or otherwise processed in a suitable manner, if necessary, and then stored in a computer memory.
Computer program code for carrying out operations of the present invention may be written in a high-level programming language, such as C or C++, for development convenience. In addition, computer program code for carrying out operations of the present invention may also be written in other programming languages, such as, but not limited to, interpreted languages. Some modules or routines may be written in assembly language or even micro-code to enhance performance and/or memory usage. However, software embodiments of the present invention do not depend on implementation with a particular programming language. It will be further appreciated that the functionality of any or all of the program modules may also be implemented using discrete hardware components, one or more application specific integrated circuits (ASICs), or a programmed digital signal processor or microcontroller.
The present invention is described above with reference to block diagram and flowchart illustrations of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the block diagrams and/or flowchart illustrations, and combinations of blocks, can be implemented by computer program instructions and/or hardware operations. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the block diagram and/or flowchart block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the block diagram and/or flowchart block or blocks.
The computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process or method such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the block diagram and/or flowchart block or blocks.
It should be noted that, in some alternative embodiments of the present invention, the functions noted in the blocks may occur out of the order noted in the figures. For example, two blocks shown in succession may in fact be executed substantially concurrently or the blocks may sometimes be executed in the reverse order, depending on the functionality involved. Furthermore, in certain embodiments of the present invention, such as object oriented programming embodiments, the sequential nature of the flowcharts may be replaced with an object model such that operations and/or functions may be performed in parallel or sequentially.
The invention will now be explained in greater detail in the following non-limiting examples.
This calibration method is based on a measurement of the phases (rather than being an optimization technique). Below is provided a theoretical background and a detailed procedure for this calibration technique.
A. Intensity Cross Section
The basis for the phase calibration technique is the intensity cross section and its Fourier Transform. Although this cross section and its transform are familiar, they are reviewed here for completeness. Shown in
B. The Fourier Transform of the Intensity
These sections provide a basic coverage of the FFT of the intensity cross section that will be used for the phase calibration. The phase of the FFT is used for the calibration but the magnitude is utilized to determine the location of the fundamental in frequency space.
1. Magnitude of Intensity FFT
The plot shown in
2. Phase of Intensity FFT
The phase over the entire range of frequency bins is shown in
3. The Phase Near the Fundamental Frequency
An enlarged partial plot of the phase (
C. Behavior of the Fourier Coefficients with PZT Voltage
This section demonstrates how both the amplitude and phase of the FFT behave with changing voltage (Phase) on the PZT. The magnitude should not and does not change as the voltage is varied. The phase shows a correlated dependence on the PZT voltage. The phase calibration technique is based on the change of the phase at the fundamental frequency with changing voltage. This meaning of this statement will become obvious in this section.
1. FFT Magnitude vs. Voltage
The magnitude of the FFT coefficients is constant over changing PZT voltage (phase). This is expected, and the plot of
2. FFT Phase vs. Voltage
The phase of the Fourier coefficients which is the arctan(imaginary/real) is shown in
It seems that all that is needed is to process the phase of the Fourier coefficient that corresponds to the peak value of the fundamental. The fundamental is located by the spatial frequency corresponding to the grid at the camera, and the Fourier amplitude coefficient having the largest value is used to determine the bin number of the phase coefficient that will be plotted vs. voltage to obtain the calibration curve. Averaging various coefficients near the peak was considered, but then a complicated unwrapping routine would be needed. Furthermore, the other coefficients seem to reveal worse behavior vs. voltage.
1. The Raw Phase Data vs. Voltage
2. The Unwrapped Phase vs. Voltage Plot
The first step is to unwrap the 2π phase discontinuity. This is done by looking for a 2π phase jump and then removing it by adding or subtracting 2π to all subsequent data points. This is done in a software loop to produce the unwrapped phase plot shown in
3. Using the Derivative to Eliminate Low Response Regions
To eliminate the undesirable low or zero response regions of the Phase vs. Voltage response function, the nearest-neighbor derivative of the data is taken.
4. Final Processed Phase Response Function
After eliminating the low response points the remaining data is plotted in
5. Deviations from Global Linear and Cubic Fits
The data from the previous section was fit to linear and cubic equations.
E. Steps in Phase vs. Voltage Calibration Procedure
The phase vs. voltage calibration can be carried out by performing the following steps:
Preliminary
Take Phase Data
Unwrap Phase Data
Calculate Derivative vs. Voltage to Establish Valid Points
Establish Phase 1,2,3 Voltages
The fidelity of the calibration can be determined by analyzing the second harmonic content of the residual lines. It has been found that the calibration error is the only thing that produces second harmonic residual lines. Therefore, the second harmonic content of the residual lines can be a metric function for the calibrations. The algorithm could be a damped optimization routine based on this merit function.
A. Calibration Merit Function Theory
Because the fidelity of the calibration is known to directly affect the second harmonic content of the imaging system data, what follows is a detailed look at this function vs. detuning of the calibration phases of the imaging system. A detailed procedure for evaluating the merit function from actual imaging system data is also discussed in this section.
1. Merit Function for Small Detuning
The trajectory through the solution on the merit function surface is V-shaped. That is, there is a linear dependence of the merit function toward the solution.
Since the maximum slope is 0.0155/degree, this should be used to determine the step size taken to determine the derivative. Since it is not desirable to go through the solution when establishing the slope, a step size should be selected that is smaller than the step that would zero out the merit function. This step size should also be small enough not cross into the nonlinear region or exit the basin of attraction.
2. Merit Function for Medium Detuning
When the cross sections of the merit function are plotted (
3. Merit Function for Large Detuning
One additional observation that this plot supports is that any value of the merit function near 0.7 could indicate that the errors may be outside of the basin of attraction. It is important that all data be taken for angular errors less than 80 degrees and merit function values not approaching the 0.7 ratio.
B. Experimental Merit Function Behavior
C. Merit Function Optimization Calibration Procedure
The following steps provide an outline for the software calibration of an imaging system using Merit function minimization:
A. For a Starting Point Characterized by:
Phases: Phase1, Phase2, Phase3
Voltages: Vphase1, Vphase2, Vphase3
1) Take imaging system trio of frames at current phase 1,2,3 settings.
2) Use one intensity frame for normalization.
3) Process imaging system trio of frames.
4) Find Second Harmonic and Merit Function.
Note that this procedure takes the derivative at the current point (point0). Corrections should be performed from this point. It is important to keep track of changes from the current state (i.e. on the derivative phases or on the current solution phases).
B. Taking the Derivative of the Merit Function at the Current Calibration Setting (see
5) Determine the phase and voltage step sizes.
6) Calculate Differential phase values.
7) Calculate Derivative voltage values.
8) Take imaging system data for phase 1 derivative.
9) Take imaging system data for phase 2 derivative.
10) Calculate Gradient Differences and Correctionfactors.
11) Calculate new values for phases and voltages to start step 1 again (steps are from point0).
C. The New Point is Characterized by:
Phases: Phase1—PhaseStepsize1, phase2—PhaseStepsize2, phase3
Voltages: Vphase1—VoltageStepSize1, Vphase2—VoltageStepSize2, Vphase3
The entire sequence is iterated until the exit condition (see step 4 g) is met. Typically, SecondHarmonicAbsolute<N*Sigma, where Sigma is standard deviation of imaging system FFT noise floor near the second harmonic.
The foregoing is illustrative of the present invention and is not to be construed as limiting thereof. Although exemplary embodiments of this invention have been described, those skilled in the art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel teachings and advantages of this invention. Accordingly, all such modifications are intended to be included within the scope of this invention as defined in the claims. The invention is defined by the following claims, with equivalents of the claims to be included therein.
| Number | Name | Date | Kind |
|---|---|---|---|
| 4629234 | Sokolowski | Dec 1986 | A |
| 4640620 | Schmidt | Feb 1987 | A |
| 5381236 | Morgan | Jan 1995 | A |
| 6239909 | Hayashi et al. | May 2001 | B1 |
| 6376818 | Wilson et al. | Apr 2002 | B1 |
| Number | Date | Country |
|---|---|---|
| WO 9845745 | Oct 1998 | WO |
