Cavity length control for Fourier domain mode locked (FDML) lasers with µm precision.

In highly dispersion compensated Fourier domain mode locked (FDML) lasers, an ultra-low noise operation can only be achieved by extremely precise and stable matching of the filter tuning period and light circulation time in the cavity. We present a robust and high precision closed-loop control algorithm and an actively cavity length controlled FDML laser. The cavity length control achieves a stability of ∼0.18 mHz at a sweep repetition rate of ∼418 kHz which corresponds to a ratio of 4×10-10. Furthermore, we prove that the rapid change of the cavity length has no negative impact on the quality of optical coherence tomography using the FDML laser as light source.


Introduction
Since the first Fourier domain mode locked (FDML) laser was introduced in 2006, there has been a steady development progress towards one of the fastest narrow band, widely tunable swept light sources available today [1,2]. Classical FDML lasers consist of a broadband gain medium, a several hundred-meter-long cavity made of different fiber types with individual dispersion coefficients (delay line), a chirped fiber Bragg grating (CFBG) and a wavelength selective element like a fiber Fabry-Pérot tunable Filter (FFP-TF). The long cavity adds a delay to the light circulation time which makes it possible to synchronize it with the tuning rate of the FFP-TF. Therefore, every sweep is seeded by the previous one in contrast to short cavity swept light sources where lasing has to build up out of spontaneous emission for every filter position [1,3]. Especially the development of highly dispersion-compensated FDML lasers reduced the instantaneous spectral linewidth, resulting in increased coherence length, reduced sensitivity decay with ranging depth (roll-off) and better image quality in optical coherence tomography (OCT) [3][4][5][6][7][8], which is the main application of FDML lasers [9][10][11][12]. The high tuning rate enables 4D real-time imaging of biological tissue even in a virtual-reality environment as our group recently demonstrated, thus opening new fields of application [2,13,14]. Further applications can be found in intravascular or heartbeat OCT [15][16][17][18][19], OCT-based micro-angiography [20] or retinal OCT [11][12][13]21]. Beside OCT, FDML lasers are used for stimulated Raman spectroscopy [22], picosecond pulse generation [23], and sensing [24][25][26][27][28][29][30][31].
In addition to dispersion correction, which is intended to ensure an equal round trip time in the cavity for all wavelengths of the frequency sweep, the continuous adjustment of filter frequency and light circulation time of the entire frequency sweep in the cavity is of significant importance for FDML lasers [32]. Even if a perfect dispersion correction is available, a mismatch can still occur, resulting in increased intensity noise and regarding OCT in a significant degradation of the image quality. This mismatch may be caused by a fluctuation in the already stabilized ambient temperature, which results in a change in length and refractive index of the fiber cavity and thus in a change of light circulation time. Then the frequency sweep exhibits more intensity dips, which is expressed by an amplified intensity noise in the signal [32]. If there is a sufficient dispersion correction and the filter frequency always matches the light circulation time, intensity noise is strongly reduced. The FDML laser is then running in an ultra-low noise operation, also described as "sweet spot operation" [32,33].
There are different approaches to ensure the desired sweet spot operation of FDML lasers despite temperature drifts. As mentioned before, the mismatch of light circulation time and filter frequency can be caused by a temperature drift of the temperature stabilized cavity. In our setup the temperature stability is about 0.01°C. The temperature dependent components of the FDML laser are typically placed inside a thermally insulated housing. Further improvements of the thermal insulation or temperature accuracy might be possible but would exceed realistic measures in terms of costs, expenses or effectiveness.
To ensure long-term sweet spot operation, until now a frequency control algorithm was used to adjust the filter frequency to the changing light circulation time in the cavity. This so called "frequency control" is currently the method of choice [32,34]. However, this causes the filter frequency to change by a few mHz. In OCT imaging, but also in every other application, where the FDML frequency is used as a clock source, the synchronization process must therefore be adapted to the constantly changing filter frequency. This can cause problems with the system integration of the FDML lasers. For instance, in time-encoded (TICO) Raman spectroscopy an unsynchronized FDML frequency and pump laser pulse would result in shifted Raman energy levels and lead to false interpretation of the spectrum [22].
The control method developed in this work uses a different approach. The cavity length is adapted to a static filter frequency by means of a motorized free space beam path (FSBP) integrated in the fiber cavity (called 'cavity length control', CLC). This approach is used on other lasers, e.g. to stabilize the repetition rate of frequency comb lasers [35]. However, these lasers usually have a much shorter cavity, so the total length adjustment needed is much smaller.
The aim is to constantly adjust the cavity length to match the varying light circulation time to the static filter frequency. If the light circulation time is decreasing, the CLC increases the FSBP-length and vice versa. This method offers several advantages compared to frequency control. The filter frequency remains constant during the entire operation and is ideally suited for synchronization processes. It is less effort to build FDML lasers since the cavity fiber length does not have to be precisely matched to the desired filter frequency. Further, it allows to build FDML lasers with adjustable filter frequencies (tuning rates).
CLC based FDML lasers may be especially useful when matching filter frequencies of two FDML lasers. If at least one of the FDML lasers is implemented with a CLC, its cavity length can be adapted to that of the other laser. Both FDML lasers can thus be operated with a common filter frequency. If the light fields of both lasers are superimposed, a beat signal is generated, from which information of the light field of a single FDML laser can be obtained [36].
In this work, we present the implementation of a functional cavity length control for FDML lasers. It includes the design of the controlling hardware, a motorized FSBP, and software comprising the control algorithm. An in-depth evaluation of the performance parameters is presented and we evaluate the influence of the active CLC on OCT image quality.

Intensity modulations as a measure for sweet spot operation
Pfeiffer et al. showed that a very low noise operating regime over the entire frequency sweep is achievable when an extremely well dispersion compensated frequency sweep and matching of light circulation time and inverse filter frequency are realized [32]. In this operating regime intensity fluctuations are hardly present. As mentioned before, if the match is lost, the frequency sweep exhibits more intensity noise [ Fig. 1(a)]. This intensity noise is formed by several intensity dips of ∼50 ps duration (referred as "holes" in the following) [ Fig. 1(b)]. An ideal frequency sweep generated during sweet spot operation would therefore show no or very few holes. With an increasing mismatch of light circulation time and filter frequency the number of holes increases holes. With an increasing mismatch of light circulation time and filter frequency the number of holes increases as well. The number of holes per timespan or per frequency sweep can be used as a measure of sweet spot operation. Unfortunately, the necessary detection bandwidth to detect the ~50 ps holes requires expensive, high bandwidth photodiodes as well as oscilloscopes exceeding 20 GHz detection bandwidth. To overcome this struggle an interferometric Mach-Zehnder setup with a path length difference of roughly 1 cm is used to detect the holes like already described in [32,34,37] with a low ~350MHz detection bandwidth. By this method it is possible to count all holes and monitor the noise condition of the laser.

FDML Setup
The FDML laser was built using a sigma ring configuration (Fig. 2). The broadband gain medium is a semiconductor optical amplifier (SOA) with a central wavelength of 1285 nm and a small signal gain of 30 dB (Thorlabs, BOA1130S). The fiber delay line (fiber coil) consists of a mixture of SMF28e+ fiber, HI1060 fiber and LEAF fiber. 80 % of the light passing the fiber coil is reflected by the CFBG and passes the delay line again. The light propagates through a total of ~487 m fiber (FSBP included) resulting in a filter frequency of 418,455 Hz. A home-built FFP-TF is used as a wavelength selective element. The polarization in the cavity can be adjusted with a motorized polarization adjuster. The fiber cavity is split between the SOA and the filter in order to implement the motorized FSBP. An optical isolator at the input of the SOA ensures unidirectional operation.  Unfortunately, the necessary detection bandwidth to detect the ∼50 ps holes requires expensive, high bandwidth photodiodes as well as oscilloscopes exceeding 20 GHz detection bandwidth. To overcome this struggle an interferometric Mach-Zehnder setup with a path length difference of roughly 1 cm is used to detect the holes like already described in [32,34,37] with a low ∼350 MHz detection bandwidth. By this method it is possible to count all holes and monitor the noise condition of the laser.

FDML setup
The FDML laser was built using a sigma ring configuration (Fig. 2). The broadband gain medium is a semiconductor optical amplifier (SOA) with a central wavelength of 1285 nm and a small signal gain of 30 dB (Thorlabs, BOA1130S). The fiber delay line (fiber coil) consists of a mixture of SMF28e+ fiber, HI1060 fiber and LEAF fiber. 80 % of the light passing the fiber coil is reflected by the CFBG and passes the delay line again. The light propagates through a total of ∼487 m fiber (FSBP included) resulting in a filter frequency of 418,455 Hz. A home-built FFP-TF is used as a wavelength selective element. The polarization in the cavity can be adjusted with a motorized polarization adjuster. The fiber cavity is split between the SOA and the filter in order to implement the motorized FSBP. An optical isolator at the input of the SOA ensures unidirectional operation.

Free space beam path
The motorized FSBP is shown in Fig. 3. Basically, the FSBP consists of two facing collimators (Thorlabs Inc., CFC8-C), one can be adjusted with a stepper motor (Nanotec Electronic GmbH & Co. KG, L2018S0604-T3,5X1) and the other is placed at a fixed position. Each collimator is mounted with the help of a mirror mount (Thorlabs Inc., KS05) to an aluminum adapter. These are mounted on two roller bearing carriers (HIWIN GmbH, MGN-Series) which are mounted on one of two linear rails. This setup ensures parallel movement of the collimator carriers over almost the entire travel distance of approximately 5 cm. The motorized collimator is driven via a spindle by the stepper motor in axial direction. Two springs, one on each side of the carriers, pull the non-motorized carrier towards the facing carrier to ensure a fixed position and reduce backlash. At each end of the FSBP a limit switch is mounted to protect the motorized components from collision with their surroundings. The stepper motor is controlled by a closed-loop stepper and a small signal gain of 30 dB (Thorlabs, BOA1130S). The fiber delay line (fiber coil) consists of a mixture of SMF28e+ fiber, HI1060 fiber and LEAF fiber. 80 % of the light passing the fiber coil is reflected by the CFBG and passes the delay line again. The light propagates through a total of ~487 m fiber (FSBP included) resulting in a filter frequency of 418,455 Hz. A home-built FFP-TF is used as a wavelength selective element. The polarization in the cavity can be adjusted with a motorized polarization adjuster. The fiber cavity is split between the SOA and the filter in order to implement the motorized FSBP. An optical isolator at the input of the SOA ensures unidirectional operation.  motor controller (Nanotec, SMCI33-1) with 1/16 th step mode resulting in a minimum step size of 0.3125 µm.
To initially set up the FSBP, the motorized collimator is positioned roughly in the middle of the FSBP. By adjusting the mirror mounts, the collimators are aligned with each other so that the coupling efficiency is maximized.

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Cavity length control algorithm
An adapted "perturb & observe" (P&O) algorithm is used as control algorithm (Fig. 4) [38]. The original P&O algorithm suffers from oscillations once the minimum of the objective function is found [39]. To overcome this, a threshold can be set to define an acceptance range for sweet spot operation. This allows for a longer undisturbed laser operation and the use of the algorithm for FDML lasers with a remaining dispersion of more than 200 fs. An adjustment of the FSBP length is only performed, if five consecutive threshold exceedances are registered. This threshold level can be set slightly above the minimum hole count if a remaining cavity dispersion is present or to zero if the dispersion compensation is done very precisely. A variable step size as a function of the hole count is used to approach the sweet spot operation with a larger step size first while successively decreasing the step size until the threshold value is reached. This is done by dividing the actual hole count by a predefined divisor. The divisor is set in such a way, that when a minor mismatch is present the step size is sufficiently high to counteract the drift with a single adjustment step. An acceptance range for the calculated step size can be set by defining a lower and upper step size limit. The lower limit is constrained by the minimum step size of the stepper motor (in our case 0.3125 µm). for the calculated step size can be set by defining a lower and upper step size limit. The lower limit is constrained by the minimum step size of the stepper motor (in our case 0.3125 µm).

Evaluation of motorized free space beam path performance
To ensure the correct behavior of the motorized FSBP two performance tests were conducted. Initially the coupling efficiency over the entire travelling distance of roughly 5 cm is evaluated for both travel directions with a step size of 185 µm. Fig. 5a shows the coupling efficiency as a function of the FSBP length for both driving directions -towards longer and shorter cavity. For both directions the maximum coupling efficiency is ~73 % (loss of 1.54 dB) at a FSBP length of ~2.5 cm. This length also marks the position where both collimators were initially aligned. The FSBP can be adjusted over a distance of ~2 cm without generating losses higher than 3 dB. With increasing losses, a proper operation of the FDML laser cannot be ensured. As evident from the graph, the coupling efficiency is independent of the driving direction.
In a second experiment, the relation of FSBP position and laser intensity noise is characterized in order to observe the objective function of the cavity length control. For this purpose, the number of holes per time interval are measured for different FSBP lengths and both driving directions (length sweep towards longer and shorter cavity) using an interferometric measurement setup. The FSBP length change is converted into an equivalent filter frequency change. A FSBP length change of +1 µm equals a filter frequency change of -0.584 mHz. The filter frequency is set to 418,455 Hz. For eight-fold optical buffering the duty cycle is set to 12.5 % as described in [40] and the forward sweeping direction is selected. The bandwidth of 100 nm is centered around 1,295 nm unless otherwise specified. The output of the FDML laser is directed into a fiber Mach-Zehnder-Interferometer with a path length difference of ~1 cm. The resulting optical interference signal is detected using a differential photodiode (DPD; Wieserlabs, WL-BPD1GA). Since FDML lasers are typically operated with a modulated SOA, like in our case, the edges of the sweep suffer from excessive noise and an increased holes count. These holes contribute to the overall holes count but do not represent the state of the intensity noise of the laser since they are present even during sweet spot operation and are caused by the SOA modulation current slopes. To avoid this problem an electronic switch is synchronized to the filter frequency but with a duty cycle of 7 % to cut out the noisy edges from the control signal. Afterwards this signal is measured with a frequency counter (FC; Keysight, 53230A) which counts the number of holes that exceed a voltage threshold of 0.3 V within a time window of 200 ms. As an additional measurement, the holes per time are also measured for different filter frequencies at a static FSBP-position in order to prove proper CLC performance and exclude effects caused by the FSBP. All three measurements, the frequency sweep and the FSBP length sweep for both directions are shown in Fig. 5b. In both measurements the temperature of the laser is stabilized to 30 °C.

Evaluation of motorized free space beam path performance
To ensure the correct behavior of the motorized FSBP two performance tests were conducted. Initially the coupling efficiency over the entire travelling distance of roughly 5 cm is evaluated for both travel directions with a step size of 185 µm. Figure 5(a) shows the coupling efficiency as a function of the FSBP length for both driving directions -towards longer and shorter cavity. For both directions the maximum coupling efficiency is ∼73 % (loss of 1.54 dB) at a FSBP length of ∼2.5 cm. This length also marks the position where both collimators were initially aligned. The FSBP can be adjusted over a distance of ∼2 cm without generating losses higher than 3 dB. With increasing losses, a proper operation of the FDML laser cannot be ensured. As evident from the graph, the coupling efficiency is independent of the driving direction.  in a rise of counted holes and therefore in an increased intensity noise. Note that the absolute number of hole count may vary depending on the coupling losses of the FSBP. However the shape of the curve is highly reproducible. It can be clearly seen that all minima are at the same position with a remaining count of ~200 holes. Starting at the minimum the slope of the right side is 2.73 times steeper than on the other side leading to an asymmetric objective function. The course of the curve is identical for all three cases which shows the correct behavior of the FSBP. Similar noise characteristics were observed for previous generations of highly dispersion corrected FDML lasers [32] and facilitate a straightforward control algorithm. In a second experiment, the relation of FSBP position and laser intensity noise is characterized in order to observe the objective function of the cavity length control. For this purpose, the

Research Article
Vol. 12, No. 5 / 1 May 2021 / Biomedical Optics Express 2609 number of holes per time interval are measured for different FSBP lengths and both driving directions (length sweep towards longer and shorter cavity) using an interferometric measurement setup. The FSBP length change is converted into an equivalent filter frequency change. A FSBP length change of +1 µm equals a filter frequency change of -0.584 mHz. The filter frequency is set to 418,455 Hz. For eight-fold optical buffering the duty cycle is set to 12.5 % as described in [40] and the forward sweeping direction is selected. The bandwidth of 100 nm is centered around 1,295 nm unless otherwise specified. The output of the FDML laser is directed into a fiber Mach-Zehnder-Interferometer with a path length difference of ∼1 cm. The resulting optical interference signal is detected using a differential photodiode (DPD; Wieserlabs, WL-BPD1GA). Since FDML lasers are typically operated with a modulated SOA, like in our case, the edges of the sweep suffer from excessive noise and an increased holes count. These holes contribute to the overall holes count but do not represent the state of the intensity noise of the laser since they are present even during sweet spot operation and are caused by the SOA modulation current slopes. To avoid this problem an electronic switch is synchronized to the filter frequency but with a duty cycle of 7% to cut out the noisy edges from the control signal. Afterwards this signal is measured with a frequency counter (FC; Keysight, 53230A) which counts the number of holes that exceed a voltage threshold of 0.3 V within a time window of 200 ms. As an additional measurement, the holes per time are also measured for different filter frequencies at a static FSBP-position in order to prove proper CLC performance and exclude effects caused by the FSBP. All three measurements, the frequency sweep and the FSBP length sweep for both directions are shown in Fig. 5(b). In both measurements the temperature of the laser is stabilized to 30°C. Figure 5(b) displays the objective function respectively the number of counted holes as a function of a mismatch of filter frequency and light circulation time ∆f. At ∆f = 0 Hz a perfect match of filter frequency and light circulation time is present. An increasing mismatch results in a rise of counted holes and therefore in an increased intensity noise. Note that the absolute number of hole count may vary depending on the coupling losses of the FSBP. However the shape of the curve is highly reproducible. It can be clearly seen that all minima are at the same position with a remaining count of ∼200 holes. Starting at the minimum the slope of the right side is 2.73 times steeper than on the other side leading to an asymmetric objective function. The course of the curve is identical for all three cases which shows the correct behavior of the FSBP. Similar noise characteristics were observed for previous generations of highly dispersion corrected FDML lasers [32] and facilitate a straightforward control algorithm.

Evaluation of cavity length control performance
The control performance on external disturbances and temperature drift is simulated by detuning the sinusoidal filter frequency and observing the control parameters. Detuning is realized by adding a periodic frequency offset to the filter frequency which may follow a triangular, a sinusoidal and a square waveform. The triangular waveform is chosen as a model for the natural drift of the fiber cavity and thus for the preservation of the sweet spot mode. It covers both drift directions and does not contain frequency jumps. Over a period of five minutes, the filter frequency is shifted by ±100 mHz, which corresponds to a drift of 80 mHz/min and a FSBP length change of ±172 µm. This drift speed is chosen approx. ten times faster than the natural drift caused by a temperature fluctuation to stress the CLC. With the same settings a sinusoidal detuning is performed as well, which not only covers both driving directions but also a changing drift speed. The rectangular waveform serves as a model for a sudden change of the filter frequency and thus for finding the sweet spot. The filter frequency is abruptly changed by 200 mHz for 9 times within five minutes. During the measurement, the length change of the FSBP and the number of holes are recorded. In all three cases the hole count threshold is set to 0 holes, the lower step size boundary is set to 0.3125 µm and the upper step size boundary to 5 µm for the sinusoidal and triangular detuning and to 200 µm for the rectangular detuning.
First, the behavior of the CLC in response to the triangle-shaped modification of the filter frequency offset is analyzed [ Fig. 6(a)]. If the number of holes is zero, the laser is considered to operate in sweet spot operation. The change in length of the FSBP shows a triangular course (red) -inversely to the filter frequency offset waveform. During the complete 5 minutes the designed control algorithm can adjust the FSBP length to follow the shift of the filter frequency. During a negative frequency shift (corresponding to a positive FSBP length change) a more even distributed lower holes count can be observed on the contrary to a positive frequency shift. This imbalance is caused by the asymmetric objective function [ Fig. 5(b)]. Despite a few outliers the ratio of counted holes at a positive and a negative frequency shift is similar to the ratio of the left and right side slope of the objective function (∼2.7). Outliers are caused by a failure of the CLC to restore the sweet spot operation by driving in the false direction and therefore increasing the hole count even more. The slope of the FSBP length change curve from 75 s to 225 s is 2.37 µm/s, which corresponds to a filter frequency drift of 83.22 mHz/min which in turn equals approximately the actual drift speed. The step size is between 0.3125 µm and 5 µm and is therefore limited by the preset step size boundaries. It would be feasible to increase the upper boundary, though the lower boundary is already set to the minimum step size of the stepper motor or more specifically of the step mode and is therefore already at its minimum. First, the behavior of the CLC in response to the triangle-shaped modification of the filter frequency offset is analyzed (Fig. 6a). If the number of holes is zero, the laser is considered to operate in sweet spot operation. The change in length of the FSBP shows a triangular course (red) -inversely to the filter frequency offset waveform. During the complete 5 minutes the designed control algorithm can adjust the FSBP length to follow the shift of the filter frequency. During a negative frequency shift (corresponding to a positive FSBP length change) a more even distributed lower holes count can be observed on the contrary to a positive frequency shift. This imbalance is caused by the asymmetric objective function (Fig. 5b). Despite a few outliers the ratio of counted holes at a positive and a negative frequency shift is In Fig. 6(b) the FSBP length change for the sinusoidal detuning is shown. As with the triangular detuning the CLC can adjust the FSBP to follow the changing filter frequency and shows the same dependencies of drift direction regarding counted holes. If the sinusoidal function approaches one of their two reversal points the drift speed changes and therefore fewer holes can be counted until the reversal point is reached and the holes count decreases to zero. This behavior can only be intensively observed for a positive filter frequency detuning. During the negative detuning a more stable number of holes is present with less pronounced drift speed dependency.
The inverse shape of the rectangular filter frequency detuning can be seen in the change in length of the FSBP in Fig. 6(c). Besides that a step function doesn't represent a realistic case of a filter frequency disturbance, however, it provides a comprehensive insight into the control algorithm performance. The step response exhibits steep falling or rising edges in response to the rectangular changes of the frequency. The time needed to restore sweet spot operation after a positive frequency jump is 1-3 s and 5-7 s after a negative frequency jump. This can also be attributed to the asymmetrical objective function. In some cases [e.g. at 100 s and 160 s, Fig. 6(c)] the CLC performs 1-2 steps into the false direction before driving in the right direction until the sweet spot operation is achieved. In the magnification of Fig. 6(c) (right) the holes count dependent step size can be seen in a decrease of the step size while approaching sweet spot position.
It is therefore possible to achieve and maintain sweet spot operation with the combination of the FSBP and the CLC especially in daily practice where the drift speed is about ten times slower. Summarizing the results above, the CLC achieves a control accuracy of 0.3125 µm concerning a cavity length of approximately 500 m of the FDML laser or ∼180 µHz in respect to a filter frequency of 418 kHz (ratio of 4×10 −10 ). The remaining holes which have an amplitude higher than 0.3 V add up to approximately 2,500 holes within 200 ms (in case of a negative triangular shaped filter frequency detuning). At 418,455 frequency sweeps per second, only every ∼30 th frequency sweep shows a hole. If a hole is approximately 50 ps long, the noise level is only increased in a time window of 50 ps. In other words, the period where holes are present is reduced to ∼0.0002% (∼200 ppm). Thus, strong noise and the resulting influences on OCT imaging can be suppressed using the CLC. This shows that the implemented control algorithm in combination with the FSBP are suitable to control the FDML laser in sweet spot operation.
To reduce the minimal step size even further we also implemented a control method with a combination of a stepper motor and a piezo actuator but we have seen that such an implementation has no significant impact on the control performance (results not shown here). On the contrary, it even caused a temporary deterioration of the laser noise characteristics due to the length reset after one of the geometric limits of the piezo actuator is reached. A more sophisticated control algorithm would be necessary to overcome this problem. As the implemented CLC showed adequate control performance using the step motor only, we decided to omit the idea of a combined stepper motor and piezo actuator control.

Recalibration quality of interferometric fringes
In swept source optical coherence tomography (SS-OCT) with FDML lasers the image quality depends, among various other factors, on the linearity of the frequency sweep before Fourier transformation and thus on the quality of the recalibration step to numerically resample the OCT raw fringe data onto an equidistance optical frequency raster. The typically MHz sweep repetition rate of FDML lasers results in fringe frequencies well beyond 1 GHz. At these high frequencies it is difficult to apply techniques like optical hardware clocking. Hence, FDML based OCT systems usually use a pre-recorded wavelength over time lookup table for the linearization step, which is then used for the following imaging session. So the question arises, if the cavity length control presented in this paper causes changes in the FDML sweep operation such that the wavelength over time sweep characteristic changes so much to cause the OCT image to deteriorate.
To investigate the influence of the control on OCT imaging, fringes are measured while the FSBP length is changed. The fringes are then recalibrated with the prerecorded recalibration fringe data recorded at standstill. For comparison, further fringes are linearized with the same prerecorded recalibration fringe data during active length control. A fast Fourier transform (FFT) of the recalibrated fringe is performed and the resulting spectrum, i.e. the axial point spread function in OCT, is evaluated. The experimental Mach-Zehnder-Interferometer setup is adapted for this purpose. The 1 cm long fiber delay section is replaced by an adjustable free space delay line consisting of two fiber collimators. The free space delay line is adjusted in such a way that the fringe frequency is held below Nyquist, resulting in densely sampled fringes.
First the CLC is switched on to establish sweet spot operation. Once this is achieved, the CLC is switched off again and a recalibration fringe is recorded. Afterwards, further 60 fringe traces are recorded over a period of 20 s while the FSBP is at standstill. The motorized collimator is then moved by 3.125 mm (corresponding to 1.81 Hz) towards longer cavity. Several iterations for each motor speed (0.62 mm/s, 1.25 mm/s, 1.88 mm/s, 2.5 mm/s) and both directions of travel are performed. In the meantime, the position of the FSBP is continuously sampled and a measurement of the fringes is triggered when passing the sweet spot position. Since the sampling of the FSBP position does not always occur when the motorized collimator passes the sweet spot position, a tolerance range of ±15.62 µm is set. This means that all fringes recorded in this tolerance range are treated as fringes from sweet spot operation. For this measurement the FDML is set to an optical bandwidth of 50 nm and a filter frequency of 417,294 Hz.
To investigate the influence of the control on OCT imaging, fringes are measured while the FSBP length is changed. The fringes are then recalibrated with the prerecorded recalibration fringe data recorded at standstill. For comparison, further fringes are linearized with the same prerecorded recalibration fringe data during active length control. A fast Fourier transform (FFT) of the recalibrated fringe is performed and the resulting spectrum, i.e. the axial point spread function in OCT, is evaluated. The experimental Mach-Zehnder-Interferometer setup is adapted for this purpose. The 1 cm long fiber delay section is replaced by an adjustable FSBP consisting of two fiber collimators. The FSBP is adjusted in such a way that the fringe frequency is held below Nyquist, resulting in densely sampled fringes.
First the CLC is switched on to establish sweet spot operation. Once this is achieved, the CLC is switched off again and a recalibration fringe is recorded. Afterwards, further 60 fringe traces are recorded over a period of 20 s while the FSBP is at standstill. The motorized collimator is then moved by 3.125 mm (corresponding to 1.81 Hz) towards longer cavity. Several iterations for each motor speed (0.62 mm/s, 1.25 mm/s, 1.88 mm/s, 2.5 mm/s) and both directions of travel are performed. In the meantime, the position of the FSBP is continuously sampled and a measurement of the fringes is triggered when passing the sweet spot position. Since the sampling of the FSBP position does not always occur when the motorized collimator passes the sweet spot position, a tolerance range of ±15.62 µm is set. This means that all fringes recorded in this tolerance range are treated as fringes from sweet spot operation. For this measurement the FDML is set to an optical bandwidth of 50 nm and a filter frequency of 417,294 Hz. In order to analyze the impact of the CLC on OCT images, the recalibration quality of the interferometric fringes was investigated for different motor velocities. Representative for all velocities, Fig. 7a shows a measured fringe for a velocity of 2.5 mm/s. The originally recorded fringes like the recalibrated fringes (Fig. 7a) show no phase jumps or intensity drops. The amplitude modulation is clearly visible due to the windowing during the recalibration process. The point spread function at 77.86 MHz has an amplitude of -6.22 dB (Fig. 7c). This maximum has a full width at half maximum (FWHM) of 1.35 MHz and a signal to noise ratio (SNR) of about 30.6 dB is calculated, which is similar to comparable FDML lasers. The sec- In order to analyze the impact of the CLC on OCT images, the recalibration quality of the interferometric fringes was investigated for different motor velocities. Representative for all velocities, Fig. 7(a) shows a measured fringe for a velocity of 2.5 mm/s. The originally recorded fringes like the recalibrated fringes [ Fig. 7(b)] show no phase jumps or intensity drops. The amplitude modulation is clearly visible due to the windowing during the recalibration process.
The point spread function at 77.86 MHz has an amplitude of -6.22 dB [ Fig. 7(c)]. This maximum has a full width at half maximum (FWHM) of 1.35 MHz and a signal to noise ratio (SNR) of about 30.6 dB is calculated, which is similar to comparable FDML lasers. The second harmonic of this frequency is at 155.36 MHz which is present in all fringe spectra. This harmonic is caused by oversaturation of the photodiode and is typically not desired in OCT imaging. However, this does not affect the results and can be neglected. The typically very weak reflections in OCT usually do not oversaturate the photodiode. Starting at a frequency of 200 MHz, a uniform noise around -82 dB is visible. The center of the point spread function, FWHM and SNR are not significantly influenced by the motion. All fringes are free of phase jumps or intensity drops and look very similar for all velocities. A minimal trend of an increase in fringe amplitude is noticeable, while the distance to the background remains equal.
The measurements prove that the velocity of the stepper motor has no or negligible influence on the recalibration of the fringes. The fringes do not show any artifacts or signal phenomena that could possibly be caused by the movement of the FSBP. This indicates that the FDML laser is robust against changes of the cavity length during the movement of the FSBP.

Assessing the OCT image quality
Lastly, the OCT image quality is assessed. For this purpose, the laser is installed in an already existing OCT imaging system, which is described in [32]. This system has a buffer stage which multiplies the frequency sweep up to 8 times. For our purpose, however, only two of three stages are used due to current system limitations. The repetition rate is multiplied by four from 418,455 Hz up to 1.674 MHz. The optical power at the output of the buffer stage is amplified with an additional SOA, so that a sample power of about 17 mW is achieved. The optical bandwidth of the frequency sweep is set to ∼100 nm. The electrical signal at the output of the photodiode (Thorlabs, PDB480C-AC) is sampled in the OCT interferometer with a sampling rate of 2 GS/s. A human fingertip and a strawberry are selected as samples. All in vivo experiments of human tissue were conducted on voluntary basis by experts of our group and approved by the Ethics Committee of the University of Lübeck. The stored raw data is then processed and saved using a custom software of our research group. The fingertip B-Scans are averaged 20-times and the strawberry B-Scans 10-times.
The OCT images of fingertip (Fig. 8) and strawberry ( Fig. 9) show already promising results with an optical bandwidth of ∼100 nm and a sweet spot of ∼90 nm. This narrower sweet spot is caused by the current non-perfect dispersion correction. Both, penetration depth and contrast are comparable to previous images acquired using a frequency controlled FDML laser with larger sweet spot and higher imaging speed [32]. Further, the background noise can be suppressed by 10-fold respectively 20-fold averaging of the B-scans. Few vertical stripes are caused by reflections at the surface and are therefore not attributable to the FDML laser. With regard to the CLC, no artifacts or image degradation can be detected. The new developed FDML Laser with the built-in FSBP does not seem to have any negative impact on OCT image quality here.
amplified with an additional SOA, so that a sample power of about 17 mW is achieved. The optical bandwidth of the frequency sweep is set to ~100 nm. The electrical signal at the output of the photodiode (Thorlabs, PDB480C-AC) is sampled in the OCT interferometer with a sampling rate of 2 GS/s. A human fingertip and a strawberry are selected as samples. All in vivo experiments of human tissue were conducted on voluntary basis by experts of our group and approved by the Ethics Committee of the University of Lübeck. The stored raw data is then processed and saved using a custom software of our research group. The fingertip B-Scans are averaged 20-times and the strawberry B-Scans 10-times. The OCT images of fingertip (Fig. 8) and strawberry ( Fig. 9) show already promising results with an optical bandwidth of ~100 nm and a sweet spot of ~90 nm. This narrower sweet spot is caused by the current non-perfect dispersion correction. Both, penetration depth and contrast are comparable to previous images acquired using a frequency controlled FDML laser with larger sweet spot and higher imaging speed [32]. Further, the background noise can be suppressed by 10-fold respectively 20-fold averaging of the B-scans. Few vertical stripes are caused by reflections at the surface and are therefore not attributable to the FDML laser. With regard to the CLC, no artifacts or image degradation can be detected. The new devel- oped FDML Laser with the built-in FSBP does not seem to have any negative impact on OCT image quality here.

Conclusion and Outlook
In this work we presented a cavity length control for FDML lasers and its application for lownoise operation (sweet spot operation). It was demonstrated that the cavity length control is capable of minimizing the overall intensity noise of the laser. Minimal cavity length changes of 0.3125 µm can be corrected which corresponds to a frequency change of ~0.18 mHz or a ratio of 4×10 -10 with respect to the filter frequency. Due to the fixed, partially adjustable frequency of the FDML laser, the cavity length control method is ideally suited for system integration where the FDML frequency is desired as a clock source. This opens new application possibilities, especially in combination with the low-noise operation.
Furthermore, we proved that the cavity length control has no influence on OCT imaging and on the fringe quality. Independent of the velocity of the stepper motor, all fringes can be perfectly recalibrated and do not differ from fringes recorded at standstill. The OCT image quality is also promising concerning the current state of the system and the displayed images exhibit high contrast and low noise. For future experiments the dispersion compensation of the cavity may be optimized in order to increase the sweet spot and thus image quality.
All in all, we successfully implemented a cavity length control for FDML lasers for the first time and proved its suitability as an alternative frequency controlling method and maintaining of sweet spot operation.

Conclusion and outlook
In this work we presented a cavity length control for FDML lasers and its application for low-noise operation (sweet spot operation). It was demonstrated that the cavity length control is capable of minimizing the overall intensity noise of the laser. Minimal cavity length changes of 0.3125 µm can be corrected which corresponds to a frequency change of ∼0.18 mHz or a ratio of 4×10 −10 with respect to the filter frequency. Due to the fixed, partially adjustable frequency of the FDML laser, the cavity length control method is ideally suited for system integration where the FDML frequency is desired as a clock source. This opens new application possibilities, especially in combination with the low-noise operation.
Furthermore, we proved that the cavity length control has no influence on OCT imaging and on the fringe quality. Independent of the velocity of the stepper motor, all fringes can be perfectly recalibrated and do not differ from fringes recorded at standstill. The OCT image quality is also promising concerning the current state of the system and the displayed images exhibit high contrast and low noise. For future experiments the dispersion compensation of the cavity may be optimized in order to increase the sweet spot and thus image quality.
All in all, we successfully implemented a cavity length control for FDML lasers for the first time and proved its suitability as an alternative frequency controlling method and maintaining of sweet spot operation.