Application Cases

Experiment Title: Digital Simulation and Control Study of Laser Interferometers

Testing Equipment: High Voltage Amplifier, Piezoelectric Transducer, Electro-Optic Modulator, Photodetector, Beam Splitter, etc.

Experiment Process:

Figure 1: Experimental Setup. Laser beams are represented by solid lines, and electrical signals are represented by dashed lines. EOM: Electro-Optic Modulator. BS: Beam Splitter. HVAMP: High Voltage Amplifier. PD: Photodetector. FPGA: Field Programmable Gate Array. PZT: Piezoelectric Transducer.

The experimental setup is shown in Figure 1. A laser beam phase-modulated at 90MHz is injected into a linear cavity, the detuning of which is driven by a piezoelectric transducer (PZT). The cavity consists of two mirrors spaced 28mm apart. The reflected light is reflected by a 50% beam splitter and detected by a broadband photodetector (PD1). The resulting photocurrent is demodulated, with the reference coming from the same local oscillator as the modulated laser. The laser transmitted through the optical cavity is detected by another photodetector (PD2), and the detected photocurrent is used as an optical power reference. The error signal and the optical power reference are sent to the I/O connector. The 16-bit analog-to-digital converter (ADC) on the I/O connector converts the above two analog signals into digital signals and inputs them into the field programmable gate array (FPGA). The digital program of the controller running on the FPGA is composed and debugged using Labview. The program output is converted from a digital signal to an analog signal by a 16-bit digital-to-analog converter, connected to the high voltage amplifier, and then connected to the cavity's PZT to drive the cavity detuning.

Figure 2: Schematic Diagram of Closed-Loop Feedback Control. G1(s) is the transfer function of the controller, and G2(s) is the transfer function of the controlled object. SP represents the set point, and C(s) represents the cavity detuning error signal. The blue part is a schematic diagram for measuring the frequency response of the measurement system.

The experiment employs closed-loop feedback control, as shown in Figure 2. The error signal of the controlled system is processed by a digital proportional-integral controller and then fed back into the cavity.

Figure 3: Frequency Response of the System.

As shown in Figure 2, the frequency response of the system is measured using a signal analyzer by injecting a sinusoidal signal into the piezoelectric ceramic and detecting the corresponding error signal. Figure 3 shows the open-loop frequency response without servo system control and the closed-loop frequency response with servo system control. It indicates that the digital control system significantly suppresses vibration noise below 1kHz. The system bandwidth is mainly limited by the mechanical resonance of the piezoelectric ceramic. Figure 4 shows the noise spectrum of the error signal in the locked and unlocked states. The peak at 1kHz indicates a slight oscillation at the edge of the control bandwidth. The background noise is measured when the Fabry-Perot cavity is not resonating.

Figure 4: Error Signal Spectrum.

Experimental Results:

Figure 5(a): Cavity transmission power and error signal with adaptive PI total gain.

Figure 5(b): Cavity transmission power and error signal with non-adaptive PI total gain.

To verify the control capability of the designed digital control system under changing laser power conditions, the incident laser is intensity-modulated with a 10Hz square wave. The experimental results are shown in Figure 5. Figure 5(a) shows the error signal and cavity transmission with adaptive total gain. Figure 5(b) shows the error signal and cavity transmission with non-adaptive total gain. The red line represents the error signal, and the blue line represents the cavity transmission power.

It can be seen that when the laser power changes, the system's transmitted light varies with the incident light, but the error signal remains zero, indicating that the adaptive total gain can effectively maintain system stability. In contrast, under non-adaptive total gain, both the system's error signal and transmitted light oscillate, indicating system instability.

High Voltage Amplifier Recommendation: ATA-7030

Figure: Specifications of the ATA-7030 High Voltage Amplifier

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