Automatic measurement of tiny length based on single chip microcomputer-based reconstruction of Michaelis interferometer

Abstract: In order to accurately and automatically measure the wavelength of He-Ne laser and the thickness of transparent film, a single-chip microcomputer is used to drive the stepper motor to drive the fine-tuning hand wheel of the Michael interferometer to rotate, so that stable interference fringes are generated on the light screen. The photodiode is used to detect the change in the light intensity of the fringing signal. The optical signal is converted into an electrical signal through the photoelectric conversion circuit and input into the single-chip microcomputer for processing. The measurement results are automatically displayed on the LCD screen. Many experiments were carried out under a general experimental environment. The experimental results were compared with the standard values. It was concluded that the modified instrument has a fast speed, small error and high accuracy in measuring tiny lengths.
Keywords: single-chip microcomputer; stepper motor; Michelson interferometer; tiny length measurement; film thickness measurement0

Introduction
Film thickness is an important indicator of film performance parameters. How to accurately, quickly and conveniently measure film thickness is of great significance in experiments. Measuring laser wavelength with Michelson interferometer is an important part of university physics experiments. During the experiment, the experimenter manually adjusts the fine-tuning hand wheel and observes the interference fringes with the human eye, which brings a lot of human errors and affects the measurement results. In order to protect the eyesight of the experimenter, improve the measurement accuracy, expand the measurement range, and promote the development of optical teaching experimental instruments, the Michelson interferometer was explored and modified based on the research of single-chip microcomputers. The
modified Michelson interferometer adds a large number of elements in electronic technology without changing the basic principles of physics, so that physics and electronic technology are well combined, and the automatic measurement of laser wavelength and film thickness is realized. The measurement is simple, accurate, and has certain practicality.

1 System working principle
The Michael interferometer based on the single-chip microcomputer performs automatic measurement of tiny lengths. The measurement objects are laser wavelength and film thickness. The system working principle is shown in Figure 1.

1.1 Laser wavelength measurement
He-Ne laser is used as the light source, and the light amplitude interference method is used. A stepper motor is used to drive the fine-tuning hand wheel to rotate instead of manual adjustment. The motor rotation angle corresponds to an optical path difference of 2△d; the "swallowing" and "spitting" stripes obtained on the light screen are converted into pulse signals through the photoelectric conversion circuit and input into the single-chip microcomputer for counting (number of stripes N), replacing the human eye to observe the stripe counting; the measurement steps, results (wavelength λ=2△d/N) and relative errors are displayed on the LCD screen, thereby realizing automatic wavelength measurement.
1.2 Thin film thickness measurement
White light is used as the light source, and the equal thickness interference method is used. The optical path principle diagram is shown in Figure 2. When the optical path difference of white light is zero, interference occurs, and the colored stripes on the light screen are converted into pulse signals through the photoelectric conversion circuit, and the initial position d1 of M1 is recorded at the same time; after the film is placed, the optical path difference increases and the colored stripes disappear; the motor drives M1 to move to the color stripes to reappear, and the final position d2 of M1 is recorded. The film refractive index n is measured by Abbe refractometer, input into the single chip microcomputer, and processed according to the formula to obtain the film thickness.

2 System structure and hardware circuit design
The system structure is mainly based on the original physical optical instrument-Michael interferometer, adding electronic technology design modules, as shown in Figure 3. The modules include: single-chip system, keyboard control unit, motor drive circuit, photoelectric conversion circuit and liquid crystal display unit.

2.1 Photoelectric conversion circuit design
The photoelectric conversion circuit consists of two parts, as shown in Figure 4, He-Ne laser interference fringe detection and white light interference color fringe detection. Its function is to convert the changing light signal into a pulse signal that can be recognized by the microcontroller.

2.1.1 Laser interference fringe detection
This part consists of two photodiodes, bias resistors R1, R2, voltage divider resistors R3, R4 and an operational amplifier A1. When the fine-tuning knob is turned, circular "swallow" and "spit" fringes will appear on the light screen. One photodiode is aligned with the center of the circular fringes, and the other is used to detect the background light. This design can greatly reduce the influence of external light intensity and can be measured under normal light intensity. The photodiode is sensitive to the changing light signal and will output a suitable electrical signal after adding the bias resistors R1 and R2. The voltage divider resistors R3 and R4 provide a suitable threshold voltage to the reverse input terminal of the operational amplifier. The electrical signal is input from the same input terminal. When it is higher than the threshold voltage Um1 of the reverse input terminal, the output voltage flips to the positive pole of the power supply voltage (+5 V). When the input voltage is lower than the threshold voltage Um1 of the reverse terminal, the output voltage flips to the ground of the power supply voltage (0 V). As a result, the "swallow" and "spit" fringes are converted into pulse signals.
2.1.2 White light interference color pattern detection
This part consists of photodiode 1, bias resistor R1, amplifier A2 and threshold comparator A3. Its principle is similar to that of laser. When color pattern appears, the change of light intensity will cause photodiode 1 to generate a weak electrical signal. This signal is amplified by amplifier A2 (the amplification factor of the amplifier is determined by resistors R6 and R7), and then passes through threshold comparator A3 (the threshold value of the threshold comparator is determined by resistors R8 and R9), and finally converted into a pulse signal.

2.2 Stepper motor drive circuit design
The stepper motor is an open-loop control element that converts electrical pulses into angular displacement. Its speed and stop position only depend on the frequency of the pulse signal. The stepper motor is used to drive the fine-tuning knob of the Michael interferometer to rotate, avoiding many human factors that interfere with the measurement. This work uses the 28BYJ-48 stepper motor, which has a small step value and improves the accuracy of the measurement.
Once the stepper motor is selected, its performance depends on the drive voltage of the motor. The higher the speed of the stepper motor and the greater the torque, the greater the current required for the motor and the higher the voltage of the drive power supply. The current flowing out of the microcontroller I/O port is too small to drive the motor to rotate, and an external driver chip is required to increase the current. The high-voltage and high-current Darlington transistor array ULN2003 is selected to drive the 28BYJ-48 stepper motor. Its working principle is as follows: when the input end is high, the output end of ULN2003 is low; when the input end is low, the output end of ULN2003 is high. The drive circuit is shown in Figure 5.

2.3 LCD display unit and keyboard control unit
The keyboard is used for data input and measurement step control. This design uses a 4×4 matrix keyboard. Compared with independent keys, the matrix keyboard greatly saves the I/O port of the microcontroller, expands the key function, and also saves hardware resources. The LCD screen is used as a human-computer interaction interface to display experimental data and measurement information.

3 Software design
Software design is the main body of measurement. The application system program design of the microcontroller is commonly used in assembly language and C language. Compared with assembly language, C language is concise, easy to use, flexible, highly reusable, and highly portable, so the system uses C language to write programs. The program flow is shown in Figure 6.

The key parts of the program are explained below.
3.1 Pulse counting program design for the photoelectric conversion part
Use the external interrupt INT0 pin of the microcontroller to detect the pulse signal obtained by photoelectric conversion. When a falling edge of a pulse arrives, the external interrupt service program is executed once. In the interrupt service program, set the variable mai_chong_ji_shu to record the number of pulses. When the interval between two pulses exceeds 50 ms, mai_chong_ji_shu increases by 1 each time the interrupt service program is entered. If the interval between two pulses does not exceed 50 ms, it means that a glitch signal has occurred, and mai_chong_ji_shu will not increase by 1. This design can remove the glitch signal.
3.2 Stepper motor drive and automatic speed regulation program design
The higher the frequency of the pulse signal that drives the stepper motor to rotate, the higher the motor speed, but the frequency cannot be too large or too small, otherwise the motor will not rotate. The motor speed can be controlled by software delay or timer interrupt method. Software delay will waste a lot of CPU resources, so the timer 0 interrupt of the microcontroller is used to drive the 28BYJ-48 stepper motor to rotate. Different initial values ​​are assigned to timer 0 to correspond to different rotation speeds of the stepper motor. If the four-way eight-beat operation mode A-AB-B-BC-C-CD-D-DA is the forward rotation of the motor, then the operation mode DA-D-CD-C-BC-B-AB-A is
the reverse rotation of the motor. Each eight-beat operation is equivalent to the motor taking one step. The design variable motor_step is specifically used to record the number of steps of the motor. The motor forward rotation variable motor_step is added, and the motor reverse rotation variable motor_step is subtracted. The motor_step value multiplied by the motor step value is the length of the Michael interferometer fine-tuning knob driven by the stepper motor.

4 Experimental results and accuracy analysis
4.1 He-Ne laser wavelength measurement
He-Ne laser with a wavelength of 632.8 nm is used as the light source. Under general experimental conditions, after a large number of tests, the system can accurately and quickly measure the wavelength length. Table 1 is the data measured by the system once.

The final result of the automatic measurement of the system is the average value of multiple measurements. As can be seen from Table 1, it is very close to the theoretical value, with an average error of 0.06%, which is much lower than the error caused by manual measurement.
The measurement error mainly comes from the measurement of △d and the fringe count N. The step value of the stepper motor is 19.53nm, which is 80.47nm smaller than the minimum scale of the fine-tuning knob of 100nm, which improves the accuracy of △d measurement, so the error is small. During the experiment, air disturbances, collisions of the laboratory table, and external vibrations will generate burr signals that affect the detection of interference fringes by the photodiode, resulting in counting errors and thus measurement errors. For smaller burr signals, they can be processed through programming without having a major impact on the fringe count, but for severe interference signals, the system cannot process them. The system will automatically determine whether the experimental error is within the allowable range based on the measurement results. If not, it will prompt for re-measurement.
4.2 Transparent film thickness measurement
The experiment selected a transparent film with a standard thickness of 80μm as the test product. The refractive index of this film was measured by Abbe refractometer, which was n=1.4294. Under general experimental conditions, a large number of film thickness measurements were carried out. Table 2 shows part of the measurement data, where d1 is the position of the moving mirror when the color stripes appear before the film is inserted, and d2 is the position of the moving mirror when the color stripes appear after the film is inserted.

From the data in Table 2, it can be calculated that the average value of the tested film thickness is 81.600 1 μm, with high accuracy (the film thickness is measured accurately to 0.1 nm level). The error in measuring the film thickness mainly comes from two aspects, the measurement of △ and n. Although the step value of the stepper motor is small, it cannot completely eliminate the error in the measurement of △, but greatly reduces it. The dust on the film inevitably affects the refractive index n of the film. During the experiment, external interference and instrument factors will affect the measurement results.

5 Conclusion
The Michelson interferometer modified based on the single-chip microcomputer can accurately, quickly and automatically measure the laser wavelength and film thickness. The non-contact method is used to measure the film thickness without damaging the film, which expands the scope of use of the Michelson interferometer and improves its practicality. The modified circuit components are inexpensive and easy to assemble. They have no effect on the manual measurement and appearance of the Michelson interferometer, which promotes the development of optical teaching experimental instruments and has certain market prospects.
This study was completed under the guidance of Liu Xingyun, a teacher from the School of Physics and Electronic Science of Hubei Normal University, with experimental equipment provided by the Optical Laboratory and the Electronic and Electrical Laboratory, and was completed through the joint efforts of the team members. I would like to express special thanks to Teacher Liu for his guidance, and at the same time express my deepest gratitude and blessings to the School of Physics and Electronic Science of Hubei Normal University and the teachers and students who provided help.