Optical frequency comb assembly and method

Abstract

Operating an optical frequency comb assembly includes operating an optical frequency comb source to generate laser light constituting an optical frequency comb and introducing the laser light into a common light path and seeding at least one branch light path by the laser light from the common light path, the branch light path comprising at least one optical element. For the branch light path, a phase difference of a first frequency mode ν.sub.1 of the optical frequency comb is determined between laser light coupled out at a reference point within the frequency comb assembly upstream of the at least one optical element and laser light coupled out at a measurement point provided in the branch light path downstream of the at least one optical element. Phase correction for the laser light from the branch light path is based on a deviation of the determined phase difference from a target value.

Claims

1. Method for operating an optical frequency comb assembly, the method comprising: operating an optical frequency comb source to generate laser light constituting an optical frequency comb and introducing the laser light into a common light path; seeding at least one branch light path by the laser light from the common light path, the at least one branch light path comprising at least one optical element; determining a phase difference of a first frequency mode ν.sub.1 of the optical frequency comb between laser light coupled out at a reference point within the frequency comb assembly upstream of the at least one optical element and laser light coupled out at a measurement point provided in the at least one branch light path downstream of the at least one optical element; and providing phase correction for the laser light from the at least one branch light path based on a deviation of the determined phase difference from a target value.

2. Method according to claim 1, wherein the reference point is the same for the determinations of the phase difference for multiple branch light paths.

3. Method according to claim 1, wherein determining the phase difference of the first frequency mode ν.sub.1 between the laser light coupled out at the reference point and the laser light coupled out at the measurement point comprises measuring a beat signal between reference light and the laser light coupled out at the reference point and/or a beat signal between the reference light and the laser light coupled out at the measurement point.

4. Method according to claim 3, wherein the reference light is continuous wave laser light.

5. Method according to claim 3, wherein the reference light is derived from the optical frequency comb provided by the optical frequency comb source to the common light path, the reference light in particular being generated by submitting the laser light to a frequency shifter and optionally carrying out frequency filtering of the laser light from the common light path.

6. Method according to claim 1, wherein the at least one optical element is configured to induce a χ(2) process and/or a χ(3) process to laser light traversing the at least one optical element and/or to amplify laser light traversing the at least one optical element.

7. Method according to claim 6, wherein the at least one optical element comprises a nonlinear frequency broadener.

8. Method according to claim 1, wherein the optical frequency comb source is in itself stabilized with respect to the offset frequency f.sub.0 and/or the repetition frequency f.sub.rep of the frequency comb.

9. Method according to claim 1, wherein the phase correction comprises modifying the optical properties of the at least one branch light path by operating at least one actuator.

10. Method according to claim 9, wherein the phase correction comprises modifying the group and/or phase delay of the at least one branch light path.

11. Method according to claim 9, wherein modifying the optical properties of the at least one branch light path by operating at least one actuator occurs via one or more phase locked loops.

12. Method according to claim 9, wherein the at least one actuator comprises one or more of a temperature modification assembly, a fiber squeezer, a fiber stretcher, a free space optical path section having adjustable length, an electro-optic device or an acousto-optic device.

13. Method according to claim 12, wherein the fiber stretcher is a piezo drum.

14. Method according to claim 1, wherein the phase correction comprises post processing of data or a feed forward scheme.

15. Method according to claim 1, wherein for the at least one branch light path a second frequency mode ν.sub.2 different from the first frequency mode ν.sub.1 is used in an application supplied with light by the branch light path.

16. Method according to claim 15, wherein the phase correction comprises a frequency-transformation step such that the phase correction provides correction at the second frequency mode ν.sub.2 used by the application, although the phase correction uses the phase difference that was determined at the first frequency mode ν.sub.1.

17. Method according to claim 16, wherein the frequency-transformation step comprises the determination of a phase difference between a portion of the laser light coupled out at the reference point and another portion of the laser light coupled out at the measurement point at two distinct frequency modes ν.sub.ref, A, ν.sub.ref, B of the frequency comb.

18. Method according to claim 17, wherein the two distinct frequency modes are at the first frequency mode ν.sub.1 and at a reference frequency mode ν.sub.1b.

19. Method according to claim 1, further comprising carrying out a reference measurement characterizing the relationship between the frequency of laser light running through the at least one branch light path and the phase difference between a portion of the laser light coupled out at the reference point and another portion of the laser light coupled out at the measurement point.

20. Method according to claim 19, comprising carrying out the reference measurement characterizing the ratio of the phase delay in the at least one branch light path for laser light at the first frequency mode ν.sub.1 and at the second frequency mode ν.sub.2.

21. Method according to claim 1, wherein light coupled out at the reference point and the light coupled out at the corresponding measurement point of a branch light path travels not more than 20 cm after being coupled out and before being used for the determination of the phase difference.

22. Optical frequency comb assembly, comprising: a common light path; an optical frequency comb source configured to generate laser light constituting an optical frequency comb and introducing the laser light into the common light path; at least one branch light path seeded by the laser light from the common light path, the at least one branch light path comprising at least one optical element; a phase measurement assembly configured to determine a phase difference of a first frequency mode ν.sub.1 of the optical frequency comb between laser light coupled out at a reference point within the frequency comb assembly upstream of the at least one optical element and laser light coupled out at a measurement point provided in the at least one branch light path downstream of the at least one optical element; and a control unit configured to provide phase correction for the laser light from the at least one branch light path based on a deviation of the determined phase difference from a target value.

Description

(1) In the following, the invention will be further described by describing embodiments with reference to the figures.

(2) FIG. 1 shows a schematic representation illustrating the concept of a frequency comb;

(3) FIG. 2 shows a schematic block diagram illustrating the method for operating an optical frequency comb assembly according to an embodiment;

(4) FIG. 3 shows a schematic block diagram illustrating the method for operating an optical frequency comb assembly according to an embodiment with a CW laser as reference light source;

(5) FIG. 4 shows a schematic block diagram illustrating the method for operating an optical frequency comb assembly according to an embodiment with the reference light being derived from the optical frequency comb source;

(6) FIG. 5 shows a schematic block diagram illustrating the method for operating an optical frequency comb assembly according to another embodiment with the reference light being derived from the optical frequency comb source; and

(7) FIG. 6 is a schematic illustration of relations between a frequency of light traversing a branch light path and a phase shift picked up by the light in the branch light path according to different models used for describing an embodiment of the invention.

(8) The present invention relates to laser light constituting an optical frequency comb. The upper part of FIG. 1 shows laser pulses 2 in a representation of the electric field against time. Both the envelope 4 of laser pulses 2 as well as the carrier wave 6 of laser pulses 2 are shown. The carrier wave 6 is represented by a sinusoidal oscillation in the range of optical frequencies.

(9) The lower part of FIG. 1 shows the optical frequency comb 8 associated with laser pulses 2 from the upper part of FIG. 1 in a representation of the intensity against the frequency. The frequency comb 8 has a plurality of laser modes, the frequencies of which can be described by the formula f.sub.m=m×f.sub.rep+f.sub.0, with f.sub.rep (repetition frequency) being a distance of neighboring modes in the frequency domain, m being a natural number and f.sub.0 being referred to as the offset frequency, in particular the carrier-envelope offset frequency, of the frequency comb 8. The modes of a real frequency comb 8, of course, extend over a finite width in the frequency domain.

(10) FIG. 2 is a schematic block diagram illustrating the working principle of the present invention. The diagram illustrates an optical frequency comb assembly 1 having an optical frequency comb source 3 that generates laser light constituting an optical frequency comb 8. The frequency comb 8 may, for example be a comb generated by fs lasers (fiber lasers, solid-state lasers, etc.), a Hz linewidth comb, a DFG comb, an electro-optic comb, a micro-resonator based comb, a comb based on photonic integrated circuits, etc. Preferably, the frequency source 3 is in itself stabilized with respect to the offset frequency f.sub.0 and/or the repetition frequency f.sub.rep of the frequency comb 8. In particular, the optical frequency comb source 3 can be a fiber laser with a fiber-coupled output port and an amplifier, such as the Menlo Systems FC 1500 system (250 MHz repetition rate, NOLM-based laser). In a preferred embodiment, a NOLM-based laser with fast actuators for locking the two degrees of freedom as described in DE 10 2014 226 973 A1 (incorporated herein by reference in its entirety) is used. The NOLM-based laser in itself is already known to be low noise. With fast actuators, this noise can be even further reduced.

(11) The laser light generated by the optical frequency comb source 3 is introduced into a common light path 5. The common light path 5 branches into a plurality (three in the illustrated embodiment) of branch light paths 7 (7a, 7b, 7c) supplied by the laser light from the common light path 5. It would, however, also be sufficient, if only one branch light path 7 was provided and supplied with light from the common light path 5. In the illustrated embodiment, the branch light paths 7 branch off from the common light path 5 at a common branching point, which, for example, may be defined by a fiber splitter. The branch light paths 7 comprise respective outputs 9 (9a, 9b, 9c), which can supply laser light to one or more applications.

(12) To specifically tailor the laser light to meet the requirements of the corresponding application, each of the branch light paths 7 comprises an amplifier 11 (11a, 11b, 11c) and a nonlinear element 13 (13a, 13b, 13c). The nonlinear elements 13 are configured to modify a frequency spectrum of the laser light going through the respective branch light paths 7 as needed for a corresponding application. The nonlinear elements 13 may have different configurations for the individual branch light paths 7.

(13) More generally, at least one optical element 11, 13 may be provided in each branch light path 7. The at least one optical element 11, 13 could be configured to induce a χ(2) process and/or a χ(3) process to laser light traversing the at least one optical element 11, 13. Alternatively or additionally, the at least one optical element 11, 13 provided in each branch light path 7 could be configured to amplify laser light traversing the at least one optical element 11, 13. This can, for example, allow tailoring the output of the branch light path 7 to the specific needs of a user. The at least one optical element 11, 13 could also be configured to induce a Raman Gain, such as a Self Soliton Raman Shift, or a Brillouin gain to laser light traversing the at least one optical element 11, 13. In particular, the at least one optical element 11, 13 can comprise a nonlinear frequency broadener. This allows generating modes for use in an application supplied by the branch light path 7. Additionally or alternatively, the at least one optical element 11, 13 could comprise the amplifier 11.

(14) The nonlinear elements 13, the amplifiers 11 and/or other optical elements of the branch light paths 7 may have nonlinear optical properties. Due to the nonlinear optical properties of specific elements provided in the branch light paths 7 and other effects, such as variations in the length of the optical path traversed by light running through the branch light path 7, phase instabilities may be introduced when the laser light traverses the branch light paths 7. The path traversed by light running through the at least one branch light path 7, in particular through the at least one optical element 11, 13 of the branch light path 7, can be subject to variations, such as environmental variations. For example, acoustic noise, temperature variations and mechanical vibrations can be especially detrimental. They all can severely disturb the light path and cause phase variations in the light that travels in the at least one branch light path 7. Since frequency is the time derivative of phase, a disturbed phase of an ideal frequency comb results in a frequency comb where the modes are frequency shifted from the original position. This effect can be at least partially corrected for according to the invention.

(15) FIG. 2 schematically shows a phase measurement assembly 15 for measuring a phase difference of a first frequency mode ν.sub.1 of the optical frequency comb 8 between laser light coupled out at a reference point R provided in the optical frequency comb assembly 1 upstream of the optical elements 11, 13 of the branch light paths 7 and laser light coupled out at a measurement point P.sub.1 provided in branch light path 7c downstream of the optical elements 11, 13. Details of the phase measurement assembly 15 will be described below. For ease of illustration, FIG. 2 only shows the phase measurement assembly 15 corresponding to the branch light path 7c. However, in an analogous manner, additional phase measurement assemblies 15 are provided for measuring phase differences between laser light coupled out at a reference point R and laser light coupled out at measurement points P2, P3 of the remaining branch light paths 7b, 7a.

(16) Using the determined phase differences between the laser light coupled out at the reference point R and the laser light coupled out at the measurement point P for each of the branch light paths 7, respectively, a phase correction is provided for the laser light from each of the branch light paths 7. As shown in FIG. 2, the phase measurement assembly 15 corresponding to a specific branch light path 7 provides the determined phase difference at the first frequency mode ν.sub.1 to a control unit 17. The control unit 17 determines and optionally also carries out a phase correction for the laser light from each of the branch light paths 7, respectively, based on a deviation of the determined phase difference for the respective branch light path 7 from a target value. The target value may be a predetermined value or may be automatically or manually determined during operation of the optical frequency comb assembly 1. Further, the target value may be the same or may not be the same for all branch light paths 7.

(17) The phase correction can compensate for time-dependent phase instabilities which, due to the frequency being the time derivative of phase, would lead to frequency shift in the comb light traversing the respective branch light path 7.

(18) In particular, the phase difference can be determined continuously or semi-continuously, for example cyclically, to be able to appropriately monitor the time evolution of the phase and take same into account for the phase correction to provide time-dependent phase correction.

(19) In the illustrated embodiment, the control unit 17 carries out a phase correction of light from a branch light path 7 by operating an actuator 19 disposed in the branch light path 7 based on the determined phase difference for the respective branch light path 7 to appropriately modify the optical properties of the branch light path 7. It would also be conceivable that more than one actuator 19 operated by the control unit 17 is provided in one or some of the branch light paths 7. For example, a temperature modification assembly, a fiber squeezer, a fiber stretcher which may be embodied as a piezo drum, an actuator for adjusting the length for a free-space optical path section, an electro-optic device, an acousto-optic device or combinations thereof may be used as actuators 19. In particular, two or more actuators 19 of different nature could be used to simultaneously provide phase correction according to two phase differences determined for light at two different frequency modes, such as the first frequency mode ν.sub.1 and another mode ν.sub.1b of the frequency comb 8, respectively.

(20) The control unit 17 may carry out the phase correction according to a closed control loop, such as a phase locked loop. In this case, the actuator 19 may be provided upstream of the measurement point P of the corresponding branch light path 7 (shown in continuous lines in FIG. 2). However, as an alternative, the actuator 19 could also be provided downstream of the respective measurement point P, as illustrated in dashed lines in FIG. 2. Then, the control scheme for carrying out the phase correction corresponds to a feed-forward scheme. Alternatively, it would also be conceivable to carry out phase correction by post processing of the data obtained by the application supplied with light by the branch light path 7, without having the actuator 19.

(21) FIGS. 3 to 5 illustrate details of the phase measurement assembly 15 according to embodiments.

(22) According to the embodiments illustrated in FIGS. 3 and 4, determining the phase difference at the first frequency mode ν.sub.1 between the reference point R and the respective measurement point P of a branch light path 7 comprises measuring a beat signal between reference light and laser light branched off at the reference point R and a beat signal between the reference light and laser light branched off at the measurement point P.

(23) According to the embodiment shown in FIG. 3, the reference light used in the beat measurements is continuous laser light provided by a highly stable continuous wave (CW) laser 21. The beat signal between the light branched off at the reference point P and the reference light from the continuous wave laser 21 is measured at a first photodiode 23, at which the light branched off at the reference point P is brought to overlap with the reference light from the continuous wave laser 21. The beat signal between the laser light branched off at the measurement point P and the reference light is measured at a second photodiode 25, at which the light branched off at the measurement point P is brought to overlap with the reference light from the continuous wave laser 21. According to an embodiment, the light from the highly stable CW laser 21 may be split at a common splitting point S and guided to the photodiodes 23, 25. Signals from the photodiodes 23, 25 are provided to the control unit 17 which based on the beat signals drives the actuators 19 accordingly to carry out phase correction.

(24) FIG. 4 shows an alternative embodiment, according to which the reference light provided to the photodiodes 23, 25 is not provided by a continuous wave laser 21, but is derived from the optical frequency comb 8 provided by the optical frequency comb source 3. The laser light is split from the common light path 5 at point U and filtered by a frequency filter 24 to one or a few modes. Optionally, the reference light can also be amplified by an amplifier 25. The laser light is then frequency shifted by a frequency shifter 27, for example an acousto-optic modulator or an electro-optic modulator, to obtain a mode that is slightly different from the first frequency mode ν.sub.1 at which the phase difference is determined. The resulting reference light is then supplied to the photodiodes 23, 25 and beat signals with light branched off at the reference point R or the measurement point P, respectively, are measured and provided to the control unit 17 as described with respect to FIG. 3. Deriving the reference light from the light provided by the frequency comb source 3 has the advantage that it is not required to provide an additional source for the reference light, such as the continuous wave laser 21. However, as the light provided by the reference comb source 3 is pulsed laser light, it has to be ensured that the pulses arriving at the photodiodes 23, 25 from the reference point R and the measurement point P are synchronized with the pulses of the reference light. In such embodiment, a multitude (typically few hundreds) of comb lines around the center value ν.sub.1 may contribute to the beat signal, and the phase of the derived radio-frequency signal will be an average phase of all contributing modes.

(25) In the illustrated embodiments, the reference point R is the same for each of the branch light paths 7. This has the advantage that the beat signal between the light branched off at the reference point R and the reference light does not have to be measured separately for each branch light path 7. Rather, one measurement of the beat signal between the laser light at the reference point R and the reference light can be carried out and used for determining the phase differences between the laser light at the reference point R and the laser light at the measurement point P of each of the branch light paths 7, respectively.

(26) In the figures, the reference point R is indicated as lying at a point where all the branch light paths 7 branch off from the common light path 5. Such implementation is convenient, as the laser light to be guided to the first photodiode 23 can be derived from an additional output of a splitter provided for splitting the common light path 5 into the branch light paths 7. However, the reference point R could also be provided at another position in the common light path 5 or even in one of the branch light paths 7 (upstream of the nonlinear optical elements 11, 13).

(27) FIG. 5 shows an embodiment that is related to the embodiment of FIG. 4. Again, the reference light is derived from the optical frequency comb 8 provided by the optical frequency comb source 3. As shown in FIG. 5, it may be sufficient to only measure the beat signal between the reference light and the laser light coupled out at the measurement point P. It is not absolutely necessary to also measure the beat signal between the reference light and the laser light coupled out at the reference point R. The laser light is split from the common light path 5 at point U and filtered by a frequency filter 24 to one or a few modes. Optionally, the reference light can also be amplified by an amplifier 25. The laser light is then frequency shifted by a frequency shifter 27, for example an acousto-optic modulator or an electro-optic modulator, to obtain a mode that is slightly different from the first frequency mode ν.sub.1 at which the phase difference is determined. The resulting reference light is then supplied to the photodiode 25 and a beat signal with light branched off at the measurement point P is measured and provided to the control unit 17. The photodiode 23 shown in FIG. 4 is not provided in the embodiment of FIG. 5. As the reference light used for measuring the beat signal between the reference light and the laser light coupled out at the measurement point P already contains information (phase information) from the frequency comb 8 supplied to the common light path 5 by the optical frequency comb source 3, measuring only the one beat signal allows determining the phase difference between light coupled out at the reference point R and the light coupled out at the measurement point P with sufficient accuracy. To increase accuracy, it is advantageous to couple out light used as the reference light from the common light path 5 near or at the reference point R (meaning that point U and reference point R are the same or near to each other). In particular, the point U at which light to serve as reference light is coupled out can also define the reference point R.

(28) As stated above, the nonlinear elements 13 of the branch light paths 7 may provide frequency modes to be used by an application supplied with light by the respective branch light path 7. That frequency mode may not be present at the reference point R. Therefore, that frequency may not be used as the first frequency mode ν.sub.1 at which the phase difference between the laser light coupled out at the reference point R and the laser light coupled out at the measurement point P of the respective branch light path 7 is determined. For one or more branch light paths 7, a second frequency mode ν.sub.2 used by an application supplied with light from the branch light path 7 may be different from the first frequency mode ν.sub.1.

(29) Preferably, the phase correction comprises a frequency-transformation step such that the phase correction provides optimal correction at the second frequency mode ν.sub.2 used by the application, although the phase correction uses the phase difference that was determined at the first frequency mode ν.sub.1. In a simple version, the detected phase difference δϕ.sub.1 at frequency ν.sub.1 can be used in the frequency-transformation step to estimate the phase difference δϕ.sub.2 at the second frequency ν.sub.2 according to the linear relation δϕ.sub.2=δϕ.sub.1*ν.sub.2/ν.sub.1. This linear relation would correspond to the dotted line shown in the diagram of FIG. 6 which shows the relation between a frequency ν of light traversing a branch light path 7 and the phase shift δϕ(T) picked up by the light in the branch light path 7. According to the linear relation shown by the dotted line, the phase difference has a frequency dependence without dispersive character.

(30) However, as group delay and phase delay or variations thereof are not generally equal in different media (except vacuum), the linear relation δϕ.sub.2=δϕ.sub.1*ν.sub.2/ν.sub.1 may be inaccurate, in particular, if the second frequency mode ν.sub.2 is far away from the first frequency mode ν.sub.1. In particular, the branch light path 7 may have normal dispersion properties, meaning that the phase delay is larger for small frequencies than for large frequencies. Although the concept of dichroic detection may be used with the described simple form of the frequency-transformation step, it can be further improved by using a more sophisticated version of the frequency-transformation step by introducing a fix point frequency ν.sub.fix, leading to the relationship δϕ.sub.2=δϕ.sub.1*(ν.sub.2−ν.sub.fix)/(ν.sub.1−ν.sub.fix), which can be used in the frequency-transformation step. The more accurate relation taking into account the fix point frequency ν.sub.fix corresponds to the continuous line in FIG. 6 showing the relation between a frequency ν of light traversing a branch light path 7 and the phase shift δϕ (T) picked up by the light in the branch light path 7 for a branch light path 7 having normal dispersion. This is more accurate.

(31) Unfortunately, for the branch light path 7 and/or the optical elements 11, 13 provided therein, in particular for most commercial fibers, dispersion properties are not well enough known to predict the fix-point frequency ν.sub.fix.

(32) To implement the improved frequency-transformation step in the phase correction, the method may further comprise carrying out a reference measurement characterizing the relationship between a frequency of laser light running through the respective branch light path 7 and a phase difference between a portion of the laser light coupled out at the reference point R and another portion of the laser light coupled out at the respective measurement point P. Using this reference measurement, the fix point frequency ν.sub.fix can be determined and the phase correction can be optimized with high accuracy at a desired frequency mode different from the first frequency mode ν.sub.1, in particular at the second frequency mode ν.sub.2. Although the results of the reference measurement allow calculating the fix point frequency ν.sub.fix, an explicit calculation of the fix point frequency ν.sub.fix is not necessary according to some embodiments.

(33) In an embodiment, the reference measurement can comprise measuring a phase difference between a portion of the laser light coupled out at the reference point R and another portion of the laser light coupled out at the measurement point P at two different frequencies to provide an improved frequency-transformation step and to allow determining the fix point frequency ν.sub.fix. In particular, the reference measurement can comprise the determination of a phase difference between a portion of the laser light coupled out at the reference point R and another portion of the laser light coupled out at the measurement point P at two distinct frequency modes ν.sub.ref, A, ν.sub.ref, B of the frequency comb 8, which in particular can correspond to the first frequency mode ν.sub.1 and a reference frequency mode ν.sub.1b. In preferred embodiments, the relative difference between the frequencies ν.sub.ref, A, ν.sub.ref, B is larger than 0.5%, more preferably larger than 2%, and even more preferably larger than 5%.

(34) Providing the phase correction for the laser light coupled out from the branch light path 7 may comprise the frequency-transformation step being based on the reference measurement and accounting for the second frequency mode ν.sub.2 being different from the first frequency mode ν.sub.1 to obtain light output from the branch light path 7 having the second frequency mode ν.sub.2 stabilized.

(35) According to an embodiment, the reference measurement can be conducted before or at the beginning of an operation of the optical frequency comb assembly 1. The fix point frequency ν.sub.fix could be determined according to that reference measurement and be used during the operation of the frequency comb assembly 1 without further adjustment during operation.

(36) The fix point frequency ν.sub.fix may depend on time, especially through time varying environmental parameters like temperature and humidity, but also mechanical stress on fibers can be a cause. Therefore, the reference measurement, according to an alternative embodiment, can be done in a continuous fashion during operation by using two frequency modes of light in the branch light path, in particular the first frequency mode ν.sub.1 and a reference frequency mode ν.sub.1b.

(37) FIG. 6 explains the physical situation underlying the frequency-correction step. The graph displays the phase delay □□(T) for light travelling in the path 7 at some chosen time T as a function of the frequency of the light. It is assumed that at the frequency ν1, the phase delay is determined according to the invention. The dotted line represents a linear estimate of the phase delay as a function of frequency, corresponding to a phase delay with no dispersive character. The straight line corresponds to a model that takes into account the dispersive character of the phase delay, here chosen to be normally dispersive. This second line traverses the y-axis at the fix-point frequency ν.sub.fix and predicts the phase shift at a second frequency ν.sub.2 in a better way. The graph also indicates a second frequency ν.sub.1b inside the range of the original frequency comb spectrum 30 which may be used to infer the slope of the model and/or the fix point frequency according to an embodiment of the invention.