METHOD OF COMPENSATING SPHERICAL ABERRATION AND CORRESPONDING ST STEM
The present invention relates to a method of, and a system for, reducing spherical abenation in optical systems. In particular, but not exclusively, the invention relates to a method and a system for reducing spherical abenation in confocal and multiphoton scanning microscopes. It is also suitable for other optical systems, for example gene chip readers and 3D optical memory systems.
It is well known that spherical abenation strongly affects the imaging performance of microscopes, and of confocal andmultiphotonmicroscopes inparticular. Spherical abenation tends to reduce the signal intensity and the axial resolution of the microscope, which in turn leads to a lower signal to noise ratio. Other optical systems may be similarly affected.
Spherical aberration can be caused by various factors, including variations in the thickness of the sample cover slip and mismatches between the nominal and actual refractive indices of the embedding and immersion media, as specified for the particular microscope objective lens. The thickness of cover slips for example is usually specified by manufacturers with a tolerance range of tens of microns, and this variation can cause significant spherical abenation. Further, the refractive indices of the embedding and immersion media are often not exactly known, as they are dependent on the chemical compositions of the media. The refractive indices are also usually temperature dependent and can vary during use from the specified nominal values, again causing spherical abenation.
Many modem microscope objective lenses, particularly those having a large numerical aperture (NA), are provided with a conection mechanism for adjusting spherical abenation. This mechanism usually includes a rotary conecting collar mounted on the lens body, which can be turned to compensate for spherical abenation. The conection collar includes an index mark, which can be aligned with a numbered scale on the lens body to apply a conecting factor based on the thickness of the cover slip. However, the precise thickness of the cover slip may not be known and the degree of spherical abenation may also be affected by other factors, such as variations in the refractive indices of the embedding and immersion media. Simple use of the numbered scale can therefore provide only an approximate conection.
The conection mechanism can also be adjusted manually by making a qualitative assessment of image quality, based for example on image intensity or contrast. However, this method of adjusting the conection mechanism is entirely subjective and therefore prone to inaccuracy. The manual adjustment process is further complicated by the fact that in most lens designs, adjusting the conection mechanism shifts the focal point of the lens, with the result that different portions of the sample are imaged, making a qualitative assessment of image quality very difficult. A further disadvantage of this method is that repeated exposure to the illuminating light can sometimes cause photo-damage to the specimen or photo-bleaching of the fluorescent material.
It is an object of the present invention to provide a method of, and system for, conecting spherical abenation that mitigates at least some of the aforesaid disadvantages.
According to one aspect of the present invention there is provided a method of reducing spherical abenation in an optical system having an illumination system for focussing incident light onto a sample, a detection system for detecting light emerging from the sample and a conection mechanism for the adjustment of spherical abenation, the method including the steps of (a) focussing the incident light onto a focal point within a sample, (b) setting the conection mechanism to a conection setting R, (c) displacing the focal point axially through a displacement z, such that it passes through at least one reflective interface of the sample, (d) measuring the intensity of light reflected from the interface at a plurality of displacement values, (e) deteπnining the axial intensity distribution I(z) of the incident light in the vicinity of the reflective interface from the measurements of reflected light, (f) determining the value of a conection criterion C(R) from the axial intensity distribution I(z), wherein the conection criterion C(R) represents quantitatively the degree of spherical abenation in the optical system, and (g), if necessary, adjusting the setting R of the conection mechanism in accordance with the determined value of the conection criterion C(R).
The method makes it possible to optimise the setting of the conection mechanism quickly and easily. The degree of spherical abenation is assessed quantitatively, making qualitative assessments of the degree of abenation unnecessary. The sample can be scanned in a region remote from the specimen, thereby avoiding the risk of photo-damage or photo-bleaching.
The conection criterion C(R) maybe determined from a subrange (zmin, zmax) of the measured axial intensity distribution I(z) of the reflected light, where the subrange contains either only one reflection or multiple reflections for which R is approximately constant for closely spaced axial positions zr.
Advantageously, the value of the conection criterion C(R) is deteπnined from the axial intensity distribution I(z) by obtaining an integral with respect to the displacement z of the measured intensity raised to a power n, where n is greater than 1. For example, the conection criterion C(R) can be determined by obtaining an integral with respect to the displacement z of the intensity I squared. By integrating the intensity squared with respect to displacement, a conection criterion can be obtained that allows the optimum setting of the conection mechanism to be identified readily.
Alternatively, the value of the conection criterion C(R) may be determined from the axial intensity distribution I(z) by obtaining the maximum value of the measured intensity. This is simpler than the first method described above, but may still be adequate in certain situations.
Advantageously, the method includes repeating steps (b) to (f) at different conection settings R, and determining an optimum conection setting R0 from the values of the conection criterion C(R) at each of the conection settings R. Preferably, the optimum conection setting R0 is deteπnined by identifying the value of the conection setting R at which the value of the conection criterion C(R) approaches a limit. The value of the conection setting R at which the value of conection criterion C(R) approaches a limit is preferably determined by a process of interpolation, using a plurality of measurements of the conection criterion C(R) at different conection settings R. The process of interpolation may include fitting a Gaussian function to the measurements of the correction criterion C(R) at different conection settings R. This allows the optimum setting of the conection mechanism to be identified quickly and accurately using only a few scans, for example three scans. The process can therefore be carried out quickly.
Advantageously, the axial displacement range z is selected such that the focal point passes through the reflective interface at each selected conection setting R.
Advantageously, at each conection setting R, the intensity of the reflected light is measured a plurality of times at each displacement z, and the axial intensity distribution I(z) is
deteπnined from an average of those measurements. This reduces the effect of noise and increases the accuracy of the method.
Optionally, the focal point may be translated laterally relative to the sample between measurements of the reflected light intensity at each displacement z. This allows the degree of spherical abenation to be assessed at various points within the area of the sample, so that the conection mechanism can be set to an optimum setting for the whole of the sample.
In a prefened embodiment, where the sample includes a specimen embedded at a finite depth within an embedding medium, the optimum setting of the conection mechanism is obtained by deteπnining optimum conection settings R;, R2 at first and second interfaces within the embedding medium, and calculating the optimum conection setting at the specific depth by a process of interpolation between the two optimum conection settings Rp R2 for the first and second interfaces, based on the depth of the specimen with respect to said first and second interfaces. This allows the setting of the conection mechanism to be optimised according to the depth of the specimen within the embedding medium. The optimum conection settings Ry, R2 at the first and second interfaces may be determined substantially simultaneously, by scanning the focal point through both interfaces.
According to another aspect of the invention there is provided a computer program comprising program instructions for causing a computer to perform the method of any of the preceding statements of invention.
The computer program may be embodied on a record medium (for example a data carrier such as a CD-ROM), stored in a computer memory (for example RAM or ROM), or carried on an electrical carrier signal (for example, distributed via the Internet).
According to a further aspect of the invention there is provided a system for reducing spherical abenation in an optical system having an illumination system for focussing incident light onto a sample, a detection system for detecting light emerging from the sample and a conection mechanism for the adjustment of spherical aberration, the system including input means, data processing means and output means, wherein the input means is ananged to receive input data representing the intensity of the detected light, the axial displacement-? of the focal point and the setting R of the conection mechanism, the data processing means is ananged to detennine the axial intensity distribution I(z) the incident light by collecting data representing the
intensity of light reflected from at least one reflective interface of the sample as the focal point is displaced axially through the reflective interface, and to determine the value of a conection criterion C(R) from the axial intensity distribution I(z), wherein the conection criterion C(R) represents quantitatively the degree of spherical abenation in the optical system, and the output means is ananged to provide output data allowing the conection setting R to be adjusted in accordance with the deteπnined value of the conection criterion C(R).
Advantageously, the data processing means is ananged to determine the value of the conection criterion C(R) from the axial intensity distribution I(z) by obtaining an integral with respect to the displacement z of the measured intensity raised to a power n, where n is greater than 1.
Alternatively, the data processing means may be ananged to determine the value of the conection criterion C(R) from the axial intensity distribution I(z) by obtaining the maximum value of the measured intensity.
Advantageously, the data processing means is ananged to determine the value of a conection criterion C(R) at different conection settings R, and to determine an optimum conection setting R0 from the values of the conection criterion C(R) at each of the conection settings R.
The data processing means is preferably arranged to determine the optimum conection setting R0 by identifying the value of the conection setting R at which the value of the conection criterion C(R) approaches a limit.
The value of the conection setting R at which the value of conection criterion C(R) approaches a limit may be determined by a process of interpolation, using a plurality of measurements of the conection criterion C(R) at different conection settings R. The process of interpolation may include fitting a Gaussian function to the measurements of the conection criterion C(R) at different conection settings R.
Advantageously, the data processing means is ananged to select the axial displacement range such that the focal point passes through the reflective interface at each selected conection setting R.
Advantageously, at each conection setting R, the intensity of the reflected light is measured a plurality of times at each displacement z, and the axial intensity distribution I(z) is determined from an average of those measurements.
The focal point may be translated laterally relative to the sample between measurements of the reflected light intensity at each displacement z.
Preferably, in an embodiment wherein the sample includes a specimen embedded at a specific depth within an embedding medium, the data processing means is ananged to obtain the optimum setting R0 of the conection mechanism by determining optimum conection settings R R2 at first and second interfaces within the embedding medium, and calculating the optimum setting at the specific depth by a process of interpolation between the two optimum conection settings R,, R- for the first and second interfaces, based on the depth of the specimen with respect to said first and second interfaces.
Advantageously, the data processing means includes a computer programmed to process the input data and deteπnine an optimum setting of the conection mechanism.
In one embodiment, the optical system includes a microscope having an illumination system for focussing light onto a sample in the microscope, a detection system for detecting light emerging from the sample and a conection mechanism for conecting spherical abenation. The microscope may be a confocal or multiphoton microscope. The invention also extends to other optical systems.
The system may include adjusting means for automatically adjusting the conection mechanism. The system may include drive means for automatically scanning the focal point of the microscope.
Certain embodiments of the invention will now be described, by way of example, with reference to the accompanying drawings, in which:
Figure 1 is a schematic side section of a microscope objective lens and a specimen mounted on a microscope slide;
Figure 2 is a schematic representation of a scan in the direction of the optical axis Z, showing various reflection interfaces;
Figure 3 is a graph showing the intensity of the light reflected from the reflection interfaces of Figure 2;
Figure 4 is a graph showing the axial intensity distribution I(z) for light reflected from a single reflection interface during a scan in the Z-direction, in an optimised situation;
Figure 5 is a graph showing the axial intensity distribution I(z) for light reflected from a single reflection interface during a scan in the Z-direction, in the presence of significant spherical abenation;
Figure 6 is a graph showing the variation of an adjustment criterion C(R) with the conection ring setting;
Figure 7 is a diagrammatic representation of an automated microscope system, including a microscope and computer;
Figure 8 is a diagrammatic representation of a graphical user interface of a spherical abenation conection system implemented on a computer;
Figure 9 is a flow chart showing the steps of a process for the continuous monitoring and adjustment of the spherical abenation setting, and
Figure 10 is a flow chart showing the steps of a process for predicting the optimum adjustment of the spherical abenation.
Figure 1 shows schematically in side section a microscope objective lens 2 having an optical axis Z.. Also shown is a sample 4, including a specimen 6 that is mounted on a slide 8 in an embedding medium 10. The specimen is covered with a glass cover slip 12, and the gap between the cover slip and the objective lens 2 is filled with, a liquid immersion medium 14, for example oil or water.
The microscope objective lens 2 includes an internal conection mechanism (not shown) of a conventional kind, for the adjustment of spherical abenation. This conection mechanism may be adjusted manually by rotating a conecting ring 16 mounted on the body 18 of the obj ecti ve lens 2. The conecting ring 16 includes a numerical scale 20, which cooperates with an index mark 22 on the lens body 18.
The lens 2 may for example be the objective lens of a conventional confocal scanning microscope, in which light from a light source (for example a laser) is focussed through the objective lens 2 onto a focal point 24 within the sample 4. Emergent light emitted or reflected from the sample 4 is collected by the objective lens 2 and focussed onto a pinhole in front of a photodetector. The microscope also includes a scanning mechanism (not shown) for scanning the focal point 24 relative to the sample 4 in the X, Y and Z directions (i.e. in orthogonal directions lying in a plane that is perpendicular to the optical axis Z, and in the direction of the optical axis). The scanning range of the microscope in the direction Z is represented by anow A.
In Figure 1 , the objective lens 2 is shown in a laterally displaced position, with the focal point 24 located within the sample 4 but to one side of the specimen 6. This is the position in which the lens is preferably located prior to scanning the specimen, during a preliminary process for determining the optimum setting of the conection mechanism to reduce or eliminate spherical abenation. During the subsequent scanning operation, the objective lens is relocated, so that the focal point 24 is within the specimen 6.
During the process for determining the optimum setting of the conection mechanism, the focal point 24 is scanned in the Z-direction, so that it passes through at least one reflective interface. This may be the interface between the embedding medium 10 and the microscope slide 8 as shown in Figure 1 , or the interface between the embedding medium 10 and the cover slip 12, or the interface between immersion medium 14 and the cover slip 12. If the focal point 24 is relocated to pass through the sample 6, it may also be possible in certain circumstances to use the reflective interface between the sample 6 and the embedding medium 10. If this is done for a fluorescent sample, the wavelength used for determining the conection setting should be one that does not excite or bleach the fluorophores within the specimen.
A proportion of the light reflected from the interface is focussed through the microscope optics onto a pinhole in front of a photodetector. As the focal point passes through each of these interfaces a distinct peak in the intensity of the reflected light can be detected, as shown in Figures 2 and 3.
To deteπnine the optimum setting R0 for the conection mechanism, the intensity I of the reflected light detected by the microscope is recorded as the focal point is scanned in the Z-
direction through one of the reflective interfaces. The axial intensity distribution I(z) can then be plotted. It should be noted that only a few (e.g. three or more) measurements of the intensity I at different axial displacements z may be required to detennine the sha e of the axial intensity distribution I(z), the full shape of the distribution being determined from those measurements by interpolation or curve fitting.
Figure 4 shows a typical axial response for an optimum situation with minimal spherical abenation, and for comparison Figure 5 shows a typical axial response in a non-optimised situation, for example where there is a mismatch between the thickness of the cover slip and the setting R of the conection mechanism. For example, in Figure 5 the thickness of the cover slip is 10 microns greater than specified, thereby producing significant spherical abenation. It can be seen that maximum intensity I of the reflected light is greater in Figure 4 and that the peak is also nanower than in Figure 5.
The variation of the axial intensity distribution I(R,z) with the setting R of the correction mechanism can thus be used to determine the optimum setting R0 of the correction mechanism. Various conection criteria C(R) can be used to detennine the optimum setting of the conection mechanism from the variation of the axial intensity distribution I(R,z). For example, at a simple level, this can be determined by comparing the peak intensity, i.e. the maximum value of I(R,z) , at various different but fixed settings R of the conection mechanism. The setting R of the conection mechanism that produces the greatest maximum then represents the optimum setting R0. Alternatively, any other method of assessing the sharpness of the peak can be used, including for example deteπnining the ratio of the height of the peak to its half-height width.
Another useful criterion is the value of intensity squared, integrated along the optical axis: i.e.
C(R) = ff(R,z)dz,
where I(R,z) denotes the axial intensity distribution and R is the conection ring setting. This criterion can then be used to locate the setting R of the conection ring where the function C(R) has a maximum. Although an infinite integral theoretically provides the greatest accuracy, in practice this would be replaced by an approximation using finite limits, zmin and zmca.
Alternatively, the intensity can be raised to any other power n greater than one: i.e.
C(R) = JP(R,z)dz, where n > 1.
To locate the setting R of the conection ring that provides a maximum for the conection criterion C(R), a number of scans are made at different conection ring settings R. The variation of the conection criterion C(R) with R can then be plotted, as shown in Figure 6. The maximum value of C(R) can be determined by interpolation, for example by fitting a Gaussian curve to the plotted values . The optimum conection ring setting R then conesp onds to the value of R at the maximum value of the fitted curve. In the example shown in Figure 6, the optimum conection ring setting is approximately 157.5.
In general, the Gaussian curve can be determined from just two or three scans, at appropriate settings R of the conection mecbanism. The settings of the conection ring for these measurements can be predetermined, based on a knowledge of the variation of the measurement criterion that is chosen.
For improved accuracy, it is helpful to average the results of several axial scans or a number of two dimensional scans, in which the specimen is translated both axially and laterally relative to the focal spot. This makes the algorithm less susceptible to noise.
The process can be implemented in a software routine that can be incorporated into the normal operating software for the microscope. An example of an automated microscope system, including a microscope and computer, is shown in Figure 7. The system includes a confocal microscope 30 having an objective lens 32 with a spherical abenation conection mechanism 34. Light from a laser light source 36 is reflected via a dichroic minor 38 and focussed through the objective lens 32 onto a sample 40. Light emerging from the sample (by reflection or fluorescent emission) is collected by the objective lens 32, passes through the dichroic minor 38 and is focussed onto a pinhole (not shown) in front of a detector 42.
The microscope also includes a scanning unit 44 for scanning the focal point in the X, Y and Z directions relative to the sample 40. The conection mechanism 34 may be adjusted manually or the microscope may include an optional drive device 46 for adjusting the conection mechanism.
The detector 42, the scanning unit 44 and the optional drive device 46 for the conection mechanism 34 are connected via an. input/output device 48 to a computer 50 that includes a
central processor 52, a memory 54, a monitor 56 and an input device 58, for example a keyboard and/or a pointing device. The computer is programmed to implement a process for reducing spherical abenation by determining the optimum setting of the conection mechanism 34. The conection mechanism 34 can then be adjusted to the optimum setting either manually or automatically, if a drive device 46 is provided.
During the process for adjusting the conection mechanism, the microscope is set up in reflection imaging configuration, so that the detector can detect light reflected from the selected interface or interfaces. This may involve removal of an emission filter (if fitted) and possibly replacement of the dichroic minor with abeam splitter, if the amount of reflected light passing through the dichroic minor is excessively attenuated. After adjusting the conection mechanism, the microscope may be set to the required imaging mode (for example, fluorescence imaging mode or reflection mode).
To operate the system manually, the user positions the sample 40 appropriately so that the chosen reflecting surface is within the focal region. The spherical abenation conection mechanism 34 is set at an appropriate pre-determined position, according to the nominal thickness of the cover slip. A scan is acquired and the computer 50 calculates the conection criterion, e.g. the integral of the square of I(z). The user then sets the conection mechanism 34 to another pre-determined position. A second scan is acquired and the computer 50 perfoπns the required calculation to detennine the conection criterion. If necessary, further settings are made and scans are taken. The computer 50 then calculates the optimum conection ring setting and displays it on the monitor 56, and the user sets the conection ring accordingly.
Alternatively, in a system where the conection ring can be adjusted automatically, for example by a drive device 46, the process can be fully automated, so that the conection mechanism 34 can be adjusted to the optimum setting by the computer 50, without any user input.
The process may be implemented in a software macro that records XZ-scans of the reflection intensity, calculates C(R) and predicts the position of the optimum setting from three single measurements, assuming a Gaussian shape for the function. A graphical user interface (GUI) 60 of the software macro is shown in Figure 8. The GUI 60 includes an upper portion 62 that is used for continuous monitoring of the spherical abenation conection setting, and a lower
portion 64 that is used when calculating the optimum setting of the spherical abenation conection mechanism. The upper portion 62 includes start 66 and stop 68 buttons that can be operated by clicking with a conventional poinϋng device, and a display window 70 that indicates the value of the adjustment criterion C(R) at the cunent setting R. This value provides the user with a quantitative indication of the image quality, a higher number representing higher quality.
The lower portion 64 includes three scan buttons 72a,b,c for different settings R of the conecting ring, each of which is associated with a display window 74a,b,c that indicates the value of the adjustment criterion C(R) at each of those settings R. The user sets the conection ring to the setting indicated on the first button 74a and clicks the button, and the computer then calculates and displays the value of the adjustment criterion C(R) in the first window 74a. This is repeated at the second and third scan settings. The lower portion also includes a "fit data" button 76 and a display window 78. After Che three scans have been completed, the user clicks the "fit data" button 76 and the computer calculates and displays the optimum conection setting in the display window 78. The user then sets the conection mechanism to this value, ensuring optimum reduction of spherical abenation.
There are two ways to operate the module. In the first mode the upper part 62 of the interface is used, and the adjustment quality is monitored close to real-time and the adjustment is performed manually. In the second mode, the lower part 64 of the interface is used, and the user sets the conection ring to three different positions, records three values and obtains a prediction for the optimum value. The prediction procedure requires calibration for each individual lens. Full automation of the optimisation process is possible if the conection ring of the lens can be controlled via the PC. In bofJh modes of the software there is no need to refocus the microscope on the specimen while a j usting the conection ring, as long as the Z- scan or scanned XZ-stack contains the reflection from the selected interface.
Since adjustment of the spherical abenation correction mechanism usually changes the focal position of the microscope, it is desirable to select the axial scan range such that it contains the reflective interface or interfaces at all selectecL settings of the conection mechanism. The appropriate sub-range or sub-ranges used for generation of the adjustment criterion or criteria C(R) can for example be centred around the ma-ximum intensity of the reflected light, and identified and traced automatically.
The same optimisation process can be perfonned using the interface between specimen and cover slip. Optimum settings for intermediate planes within the specimen volume can then be infened by linear interpolation between the settings for the bottom and top of the specimen.
The steps of a semi-automatic computer-implemented process for continuously monitoring and adjusting the spherical abenation conection mechanism according to the first mode of operation are shown diagrammatically in the flow chart of Figure 9. In the first step 80 of the process, the initial values are set for a scan range that will include a reflection interface for any setting of the conection ring. In the second step 82, the microscope is scanned so that the focal point passes through the reflection interface in the axial direction, and the axial intensity distribution I(z) is recorded. The conection function C(R) for the cunent conection setting R is then calculated 84. This value is displayed 86 to the user. The user reads the cunent value of the conection criterion and optimises it, using a selected criterion. If for example the integral of the squared intensity is used as the criterion, the user maximises the value of C(R) that is displayed 86 by cyclical repetition of the steps 90, 82, 84, 86 and 88. When the user is satisfied with the cunent setting, optimisation of the spherical abenation adjustment is concluded 92.
The steps of a second operational mode of a computer-implemented process for predicting the optimum adjustment of the spherical abenation conection mechanism are shown diagrammatically in the flow chart of Figure 10. This process includes a first step 100 in which the initial values are set for a scan range that will include a reflection interface for any setting of the conection ring. In the second step 102, the spherical abenation conection mechanism is adjusted to a setting that should allow the conection function C(R) to be Obtained. The reflection interface is then scanned 104 in the axial direction and the axial intensity distribution I(z) is recorded. The conection function C(R) is then calculated 106 and its value is stored. The number of values of the conection function that have been obtained is then assessed 108. If an insufficient number of values have been obtained, the process returns to the second step 102 and another value is obtained. If a sufficient number of values of the conection function have been obtained, these are fitted to a model of the conection function and the optimum setting of the conection mechanism is deteπnined 110. This value is then displayed 112, so that the user can set the conection ring to the optimum value.
Many microscopes are used with a selection of objective lenses that may have adjustable spherical abenation conection mechanisms. The criteria described may have different functional fonns for each model of lens. The required' information for each lens could therefore be included in a software database to be recalled whenever that lens is used.
If the refractive index of the specimen is different to the nominal refractive index for which the objective lens was designed then the optimum setting of the spherical abenation conection mechanism will be different for imaging at different depths within the specimen. Since the amount of spherical abenation depends linearly on focussing depth, an interpolation method may be used. Firstly, the above conection scheme is applied to the reflection between the cover-glass and the embedding medium and the optimum conection setting is noted. Secondly, the conection scheme is applied to the reflection from the interface between the embedding medium and the microscope slide and the optimum conection setting is again noted. For imaging in intermediate planes, the optimum setting; can be calculated as a linear interpolation between the two noted settings. This process can be integrated into the software.
Since this approach uses reflected light, it is possible to use a wavelength for the adjustment that does not excite the fluorescence in the specimen. In this way, the detrimental effects of photo-bleaching can be avoided.
Despite the remarks in the previous paragraph, the approach could also be applied to fluorescent signals as well as reflected light signals. For example, a fluorescence arising from the bottom of the cover glass and/or on the top of the microscope slide could be used. This fluorescence could arise from a layer or a group of fluorescent beads. Further, the fluorescence labelling of the specimen could also be used.
The system and method described herein are also suitable for use in other optical systems than microscopes, including for example gene chips readers and 3D optical memory systems.
Although the embodiments of the process described with reference to the drawings are implemented by computer apparatus, the invention also extends to computer pro grams adapted for putting the invention into practice, and in particular to programs embodied on a record medium (for example a data canier such as a disk, tape or CD-HOM), stored in a computer memory (for example in RAM or ROM), carried on an electrical carrier signal (for example, distributed via a network or the Internet) or embedded in an integrated circuit.