New electronic implementation of the timestamps method intended for high resolution comparison of laser wavelengths

This equation shows that the precision of the measurement of the unknown wavelength λ_U depends critically on the ratio of the number of measured interference fringes. It is assumed the same refraction index for both wavelengths, but if needed, a correction factor can be applied to improve the precision of the wavelength calculation.

We have developed a first prototype of wavemeter based on the Vernier method.^3,4 For this development, several uncertainty factors have been considered,^5,6 such as the laser beams divergence and misalignments. The refractive index of the air for each wavelength has been calculated using Eldén’s equation based on a network of sensors that provide precise measurements of the temperature, atmospheric pressure P, and relative humidity.

The measurement of the number of fringes requires an electronic system with enough speed and resolution. The signal provided by the photodiodes is sinusoidal with a typical amplitude of a few millivolts and frequencies ranging from a few kHz to MHz depending on the speed of the mobile arm. The signal carries noise from the optical and electronic elements and must be amplified and filtered to provide an input level suitable to trigger the digital circuits. In our system, we have limited the frequency to 100 kHz, but this value will be improved in the future.

This article describes a new electronic system that counts the interference fringes with a high fringe resolution and calculates the unknown wavelength with good accuracy. Based on the experience of the first prototype, we have proposed a new measurement method based on the timestamps⁷ and multicoincidence⁸ methods. The new hardware is composed of a control board and a high speed counter module. The microcontroller used (Atmel AT89S52) is an updated version of the classic 8051 family that allows in-system programming (ISP) and many other improvements. We have considered other solutions such as FPGAs or alternative microcontroller boards, but we have chosen this configuration for compatibility with previous developments.

The high speed counter module uses registers and counters to acquire the timestamps with the required time resolution and transfer data to the microcontroller. This approach allows the use of many microcontroller boards with a broad range of processing speeds, eliminates real time requirements, and simplifies software development. This module reaches a resolution of 10 ns for a 100 MHz oscillator, and it could be improved by the use of faster logic families and higher clock frequencies.

In the next paragraphs, we make a review of the techniques used in existing systems.

The simplest case of wavemeter was proposed by Scholten et al.,⁹ and it was designed to count only an integer number of fringes of both lasers. The electronic system is made of binary counters and other basic digital circuits. In these circumstances, the error can be as high as a complete fringe period, which can be solved by increasing the number of fringes by means of a larger displacement of the mobile arm of the interferometer, which is difficult to achieve because of the misalignment problems in the interferometer. The authors report a relative accuracy of 3.8 × 10⁻⁶ of a fringe for a number of fringes around 650 000.

This system was improved by Ugray et al.,¹⁰ using a PIC18F1320 microcontroller running at 40 MHz.

One way of increasing the number of fringes^1,11 and the resolution is by multiplying the fringe signal frequency with a Phase Locked Loop (PLL) electronic circuit. This method requires precise control of the displacement of the mobile arm of the interferometer to achieve a high frequency stability of the fringe signal. Using a multiplying factor of 128, resolutions in the range of 8 × 10⁻⁹ of a fringe are obtained with a scan range of only 165 mm.¹¹ 

The Vernier method¹² counts the fringes between two phase coincidences of the signals, lowering the error due to truncating N_R and N_U to integer numbers. In this situation, the precision depends on the electronic circuits employed to detect the phase coincidence between the signals. This method has the disadvantage that the measurement length is limited to points where there is a phase coincidence, and sometimes the measurement cannot be made when the coincidences cannot be detected. The authors achieved a precision in the range of 1 × 10⁻⁸ of a fringe and report that the main source of error is the amplitude noise that affects the zero crossing points of the digital signals.

Ishikawa et al.⁸ improved the Vernier method by extending the counting of fringes to a set of successive phase coincidences. The system is made of counters and latches that store the number of fringes for each input. Every time there is a coincidence, the values of both counters are latched and transmitted to a computer. At the end of the process, the computer stores a total number of 2N coincidences and calculates the coefficients N_R/N_U for pairs of values separated by N/2 coincidences, and it averages all coefficients.

This method reduces the error by a factor N^1/2, and the uncertainty is 1/500 of a fringe, obtaining a resolution better than 1 × 10⁻⁹ of a fringe.

The main disadvantages of this system are the poor resolution of the detection logic (≈300 ns) and the transmission time (≈15 ms), which limit the number of coincidences that can be captured and can cause data loss.

An improvement of the system was described by Bennet and Gill,¹³ measuring the fractional part of the fringes at the beginning and end of the scan. They used different sets of digital counters (seven and three digits), flip-flops, and a 5 MHz oscillator. The method consisted of counting the integer number of fringes with the seven digit digital counters and measuring the time intervals between zero crossings of both signals with the three digit counters. The circuit also measured the initial and final periods of the signals. For a 50 kHz maximum fringe frequency and 1 000 000 fringes, a resolution of 10⁻⁸ can be achieved. This method had the disadvantages of low flexibility, low fringe resolution, and that the logic registers could only store a maximum of 6 parameters corresponding to the total number of fringes and fractional parts at the beginning and end of the counts. Any improvement of these limitations involved a complete redesign of the measurement system.

Monchalin et al.¹⁴ improved this method using a computer (PDP12) and a crystal clock to calculate the phase differences. This method obtains local measurements at different times during the scan to check the uncertainty of the process, but the computer employed is very old. The crystal clock has a frequency of a few hundred kHz, which is better than the 50 kHz clock used by Bennet and Gill. With these improvements, they achieved a resolution of 2 × 10⁻⁹ of a fringe.

Pedregosa et al.⁷ proposed a new method for phase measurement using commercial data acquisition boards that allows the storage of timestamps for each pulse of the fringe signals. They used an interferometer with a displacement of 40 cm and a PCIe-6363 acquisition board combined with a HM-8122 digital counter as an adaptor for converting the analog pulses to a digital signal. The acquisition board has a 100 MHz internal clock that allows a time resolution of 10 ns. The internal memory of the card stores the timestamps of both signal pulses, which provide information about the total number of fringes as well as the time differences at the beginning and end of the acquisition. The authors report a precision of 10⁻⁸ of a fringe (high-speed mode) and 10⁻¹⁰ of a fringe (low-speed mode). The main advantage of this method is that it provides a large quantity of information used to verify the reliability of the measurements. Its disadvantage is the high price of the equipment (acquisition card and digital counter), which could be replaced by cheaper electronic circuits.

In this paper, we present a new measurement method that improves the resolution and eliminates some of the disadvantages of the traditional methods while having a lower cost and higher flexibility. We have called this new method “multicoefficient fractional counting” because it counts the fractional parts of the fringes like in Bennet and Gill¹³ and also uses timestamps like Pedregosa et al.⁷ The hardware is a combination of high-speed elements with a common microcontroller for interfacing and a computer for data processing. The complete system is easily repeatable at a reduced cost. The measurement process is similar to the multicoincidence method of Ishikawa⁸ but without the need to wait for phase coincidences, which allows us to begin and end the capture process at any point during the scan. This maximizes the measurement length of the interferometer and reduces the hardware complexity because there is no need to detect phase coincidences with high precision.

The measurement process is a modified version of Bennet and Gill.¹³ Our process starts with the acquisition of two initial timestamps for the reference and unknown signals. Then, a large number of integer fringes (N and M) are counted and two final timestamps are also stored for both signals. These data provide all the information needed to calculate the numbers N_U and N_R with precision. The intermediate timestamps are not stored.

Figure 2 shows the position of the captured timestamps, where λ_U and λ_R are the unknown and reference wavelengths, t_U and t_R are the unknown and reference timestamps, and N and M are the total number of pulses of the unknown and reference signals. The values N and M are integer numbers of pulses and coincide, respectively, with N_U and N_R in Eq. (1) when there is a phase coincidence at the beginning and end points.

The system can also acquire timestamps at any time during the scan, which allows us to check the local fringe frequency, control the displacement speed, and check the noise and quality of the fringes. The timestamps can also be used to detect phase coincidences (like in the Vernier method), with the advantage that the system can calculate the phase at any given time and even predict future coincidences.

If many timestamps are stored during the scan process, the information provided can be used to calculate a large number of λ_U/λ_R ratios instead of a single value with the initial and final data. This method has been used by Ishikawa,⁸ but only between coincidence points in the signals. We have extended the method to any point during the scan, calculating the wavelength ratios with many sets of timestamps equally spaced. The time difference between the timestamps should be large enough to have a number of fringes greater than 1 000 000 to achieve a good measurement resolution.

The system continuously acquires timestamps, which are transmitted and stored on a computer to start the offline calculation process. The method consists of calculating the wavelength ratios using Eqs. (2) and (3) for timestamps separated by a long interval. For example, with 1 000 000 fringes, the fractional parts are calculated by the timestamps 1 and 1 000 001, 2 and 1 000 002, and so on. This process is repeated for a large number of successive pairs of timestamps. Finally, the mean value of the ratios is obtained to reduce the error, like in the Ishikawa method. The interval between maximum and minimum values provides an insight into the quality of the measurements. The graphical representation of the whole set of values helps to identify problems during the scan. As an example, Fig. 3 shows a representation of 250 frequency ratios λ_U/λ_R calculated in one of the test measurements with two oscillators of 5.86 kHz (obtained from two quartz crystals of 6 MHz nominal frequency). The results show a relative error between the two frequencies of 2.1 ppm.

Our design implements the timestamps method with a low-cost electronic module composed of a general purpose microcontroller and a new high-speed interface module that provides a good time resolution in the timestamps capture.

The block diagram of the complete system is shown in Fig. 4. The optical system is composed of a Michelson interferometer with a mobile arm driven by an electronic stage, a reference laser and an unknown laser whose frequencies are compared, and auxiliary elements, such as filters and beam splitters. The analog electronics are composed of two photodetectors, analog amplifiers and filters, and Schmitt-trigger comparators made with operational amplifiers.

This part of the system was described in detail in previous studies by the authors.^3,4 For the current prototype, we have chosen to use the same analog module because it has been used in our previous development and tested in a real Michelson interferometer with good results.

The analog module is composed of two identical sections for each laser, composed of a photodiode, a transimpedance amplifier, a voltage preamplifier with filter, a variable gain amplifier, and a Schmitt-trigger comparator. The sections are AC coupled by capacitors to compensate for the differences in the medium level of the optical signals. The combined effect of the amplifiers and comparators works as a zero-crossing detector, which eliminates the problem of the different amplitudes and rise times of the signals. All the circuits used the same 5 V positive supply, and a LDO LP2950 regulator generated a 3.3 V reference supply for the reverse polarization of the photodiodes. This configuration allows that a single supply can be used for all the analog circuits, although the power supply has separate outputs with different regulators to avoid feedback between the different amplifier stages. The digital circuits have a different power supply with a LM2576 switched regulator. The TLE2074 operational amplifier has been used in all the stages because of its good characteristics of low noise, bandwidth, and slew rate.

We have made electronic and optical tests to verify this module. It has been integrated into a real Michelson interferometer at LOMG Laboratory, with a reference laser (Research Electro-Optics model 32734) and a second laser (HP 5519A) to measure its uncertainty. The results agreed with previous measurements made at the Metrology Laboratory of the ETSII at the Technical University of Madrid (UPM).

Figure 5(a) shows the schematic of the analog module with the transimpedance and inverter amplifiers, and Fig. 5(b) shows the variable gain amplifiers and Schmitt-trigger amplifiers.

The high-speed interface module is composed of a double set of counters and registers, which store the timestamps for each input pulse of both signals. These values are read by the microcontroller, which creates a record for each timestamp that includes the acquisition time and fringe number. The microcontroller stores a certain number of records in its internal memory and transmits them to a computer when required. The number of records has been limited to 16 measurements to reduce the memory requirements of the microcontroller, but it can be increased using a different microcontroller or an external memory module.

This method combines the high speed of the hardware counters with the flexibility of the microcontroller at a low cost and with good performance.

This module has been designed at Escolas Proval High School and serves as an assembly and soldering practice with surface mount devices (SMD) for the students of vocational training.

Figure 6 shows the block diagram of the high-speed interface module and its connection to the microcontroller, and Fig. 7 shows the electronic schematic of the module.

The high-speed interface module has been made with a 100 MHz crystal oscillator and 74AC161 synchronous counters. All the logic circuits belong to the AC (Advanced CMOS) logic family because this technology has the speed, low power, and reduced cost required for this application. A set of 74AC574 registers stores the instantaneous values of the counters and serves as the interface to an AT89S52 microcontroller. The counters provide the lower 16-bits of each timestamp, and the microcontroller generates by software the higher 16-bits; thus, each timestamp is 32-bit wide. These software-extended counters can generate timestamps between 0 and 42 s (with a 100 MHz clock), which is long enough for typical scan times. Anyway, the counters can be extended by software to 48-bits or more if needed for longer measurement times or interferometer lengths.

The resolution of the system depends on the period of the main oscillator (10 ns for a 100 MHz crystal). This value could be increased in future versions of the hardware to improve the resolution of the system or reduce the acquisition time.

The two digital signals are applied to the clock input of the registers and latched into flip-flops that generate interrupts for the microcontroller (one for each channel). When the register clocks are activated, they store a 16-bit value that represents the lower part of the timestamp. At the same time, the associated interruption is activated. The microcontroller performs two operations: it reads the registers and completes the value with the upper 16-bits (generated by a software counter) to form a 32-bit timestamp, and it updates the associated fringe counter and stores its value.

The registers and counters are different for each channel, so the input pulses can be simultaneous without data loss because they are stored separately.

The acquisition process stores a group of 16 consecutive timestamps for each channel. Each time the memory buffer reaches its maximum value, the data are transmitted to the computer by a USB connection. During this time, the fringe counters are updated by the microcontroller to maintain the continuity of measurement.

This method of measurement requires a small space of memory in the microcontroller, whereas the computer receives and processes a large amount of data that lets us make precise wavelength calculations.

The first and last sets of timestamps have the information required to calculate the fractional parts of the fringes like in the Bennet–Gill method.¹³ In our method, the resolution is not limited to 10⁻³ parts of a fringe by the number of digits of the counters; in fact, it could be as large as desired by reducing the fringe frequency. In our case, the reference oscillator is a 100 MHz one instead of the original 5 MHz.

This method does not require a constant velocity of the interferometer or a constant frequency in the input signals, like methods based on frequency multiplying with PLL circuits, because each set of timestamps provides information about the local frequency at any time during the acquisition. This information can be used as a quality measurement of the input signals or to control the speed of the mobile arm of the interferometer.

The high-speed interface module has been designed to interface with a low-speed microcontroller without data loss. Three groups of flip-flops detect the synchronization signals (two input signals and the counter overflow) and remain enabled until the microcontroller recognizes and disables them. This solution has been adopted because some events (like the overflow of digital counters) can be too fast to be recognized by the microcontroller if they are directly coupled.

The control program has been designed around three interrupt routines that look after the events produced by the high-speed module. Two of the interrupt routines deal with the detection and storage of the timestamps of the input signals, and the third routine detects the overflow of the digital counters and updates the 32-bit software counter.

The main program performs the tasks of communication with the computer, reads a four switch keyboard, and controls an LCD screen.

The code has been written in assembly language to optimize size and speed. All routines have been made as short as possible to avoid delays, especially the interrupt service routines. We had to solve some critical problems, like the coincidence of the overflow signal of the hardware counters with the input pulses in one or both signals. In this case, the program checks the values of the hardware counters to determine if the overflow was produced before or after the input pulse of the signal and applies a correction if needed.

One of the tests has been the measurement of the maximum duration of the interrupt routines of the input signals because this time limits the maximum input frequency. For an oscillator frequency of 30 MHz, this time results in 66 µs (considering the worst case, which is the accumulated time of the three interrupt routines). This time is the minimum period of the input signals, and the maximum input frequency results in 16 kHz.

The interrupt time is also limited by the overflow time of the hardware counters. For an oscillator of 100 MHz and a maximum count of 65 536 cycles, the overflow time is 655.36 µs, which is higher than the input period calculated before. This guarantees that all overflow pulses are correctly processed by the microcontroller.

The process of electronic testing of the high-speed interface module has been carefully designed in several steps: an initial hardware check to make sure all the circuits work properly and send data to the microcontroller, a self-diagnostic program in which the microcontroller generates signal pulses for the high-speed module and reads the data, and finally tests with single and double external oscillators. The results of these tests have served to detect some problems in the design, and a new version of the board has been made to correct them.

After assembly of the board, an external signal generator was connected simultaneously to the counter’s clock (without the 100 MHz oscillator) and the two fringe inputs. A finite number of pulses was applied to the inputs, and the microcontroller read the register values to verify that the number of pulses was correct.

After this test, the crystal oscillator was connected and the signals in the counters were checked with an oscilloscope to measure the delays.

The results of these tests have served to detect some problems, such as the counter propagation delay and overflow signal latching, that have been fixed in the current hardware.

This option has been included in the measurement program and can be used at any moment to check the correct operation of the system. This mode works almost like a real measurement because the timestamps are stored and transmitted to the computer, and the number of pulses is also counted. The microcontroller produces a digital signal that must be connected to both inputs of the high-speed interface module. Depending on the exact time in which the pulses are captured, one of the inputs can be slightly advanced or delayed with respect to the oscillator pulses. The microcontroller checks the timestamps and sends data to the computer only when there is a difference between them. In normal operation, the difference can only be 0, +1, or −1 (most of the data should coincide). Other values (2 or more) mean that there is a large delay in acquisition or a malfunction in the counters or registers operation.

A large number of tests have been made to check the operation of the module. These tests have revealed problems in the interrupt routines when a counter overflow coincides with signal pulses, and as a result, a new version of the program has been developed that corrects these issues.

Figure 8 shows a graphical representation of the timestamp difference for 500 000 pulses. Only 142 timestamps have different values, and all of them are in the range (−1, +1), which means that the module is working as expected.

These tests consist of applying one or two external digital signals to the inputs and calculating their frequency (or wavelength) ratio. The frequencies have been chosen around 10 kHz (less than the maximum value of 16 kHz) to achieve a resolution of 10⁻⁴ in each fringe, and initial and final timestamps for each measurement are separated by a minimum number of 10⁶ fringes. For these tests, we have used the test oscillator described in Ref. 4 and a signal generator Rigol DG-1022.

As these electronic signals are usually described by their frequency (instead of the wavelength used for optical signals), in the next paragraphs we will refer to “frequency ratios” instead of “wavelength ratios.”

The first test was made with the same signal in both inputs and a frequency of 5.86 kHz (obtained from a crystal oscillator of 6 MHz and a division factor of 1024). A total number of 1000 ratios were calculated. For clarity, Fig. 9 shows only the first 250 ratios and the small variations (±5.8 × 10⁻¹¹) produced by the local differences in timestamp values.

The mean value of 1000 ratios was also calculated, and the resulting error was 5.9 × 10⁻¹⁴, so the error is greatly reduced with our method based on multiple ratio calculations.

The second test was made with the signal generator adjusted to produce two slightly different frequencies (10 000.00 and 10 000.01 Hz) and connected to the input channels. Figure 10 shows the first 250 frequency ratios and their statistical distribution, showing the deviation from the theoretical ratio of 1.000 001. In this case, the error is greater (1.6 × 10⁻¹⁰), probably due to small variations in the generator output. After calculating the mean value of 10 000 ratios, the resulting error is 5.6 × 10⁻¹³, which is also much better than a single measurement.

We have also calculated the local frequencies in both channels using timestamps between consecutive transmissions. This measurement has a higher variability due to the small amount of fringes used, but it is useful to control the speed of the interferometer and check the noise of the system. Figure 11 shows a representation of the local frequency estimations and their statistical distributions.

The mean values result in 10 000, 15 924 Hz and 10 000, 14 866 Hz, which are slightly higher than the expected values. The difference (0.0015%) can be explained by the frequency tolerance of the crystal oscillators of the signal generator and the high-speed module, with typical values of 0.0025% (25 ppm) or more.

It is planned to make improvements in the system to achieve better resolutions and reduce acquisition times. The clock frequency of the counters can be increased to 200 MHz or more using CMOS technologies with delays lower than 5 ns like LVC or LCX. For the microcontroller, it is planned to use single-cycle models, such as AT89LP52 (8051 family) or Atmega644P (Atmega family), that also have more memory for programs and data.

As new possible applications, we could include the comparison of electronic oscillators, for example, to calibrate quartz crystal oscillators used in electronic instrumentation such as function generators or frequency meters.

Another possible electronic application is the precise pairing of the transmitter and receiver oscillators in Low Power Wide Area (LPWA) communications systems using narrow-band modulations, such as LoRa, SigFox, or NB-IoT, where the frequency deviation is a critical factor. These systems have a broad field of application for remote acquisition of sensor data and satellite communications.^15–18 

In this paper, we present the development of a new measurement system for the comparison of two electronic signals of different frequencies with intended application to high resolution laser wavelength comparison.

The system has been tested with electronic signal generators, and its future application could be the calibration of laser diodes with a reference laser using a Michelson interferometer.

A high-speed module has been developed to interface with a broad range of microcontrollers and allows the acquisition of timestamps at any time during the scans, detects phase coincidences like in Vernier method,¹² or checks the signals’ frequencies to control the interferometer displacement.

We have developed a new measurement method called the “multicoefficient fractional counting method” based on the timestamps and multicoincidence methods. This method uses a large number of consecutive measurements to reduce uncertainty.

The new electronic prototype achieves a precision of <10⁻¹² in the calculation of the ratio of the signals’ frequencies, much better than our previous development based on the Vernier method (<10⁻⁸), with easily accessible components at a very low cost. This result is based on a 100 s acquisition time with a test frequency of 10 kHz, a time resolution of the electronic circuits of 10 ns, 10⁶ signal cycles, and averaging 10⁴ consecutive measurements.

Our system has no limit on the number of counted cycles or the fractional parts resolution like in Bennet and Gill,¹³ whose hardware has a limited counting capacity; thus, acquisition time cannot be increased. In addition, the frequency of the reference oscillator has been increased by a factor of 20 from 5 to 100 MHz.

Our system does not require expensive computers or data acquisition cards like the timestamps method by Pedregosa et al.⁷ There is no need for exact phase coincidence of the signals, which allows the measurement to be made at any point of the displacement of the interferometer, maximizing the useful length. Moreover, our system does not require a constant velocity of the interferometer or a constant frequency in the input signals like methods based on PLL circuits.¹¹ This advantage simplifies the design of the optical system and considerably reduces its cost.

The low cost of the hardware and software developed has allowed it to be used for practical lessons in electronics and programming subjects in vocational training or university degrees. The obtained results provide us with an important tool for our research laboratory.

The assembler code of the microcontroller program is provided as the supplementary material in the following link.

The authors would like to acknowledge the Government of Galicia for funding the No. 15AELE02 Vocational Training Innovation Project.

The authors have no conflicts of interest to disclose.

Javier Diz-Bugarín: Conceptualization (lead); Funding acquisition (lead); Investigation (lead); Methodology (lead); Project administration (lead); Software (lead); Validation (lead); Writing – original draft (lead); Writing – review & editing (lead). Ismael Outumuro-González: Investigation (equal); Resources (equal); Supervision (equal); Validation (equal). José Benito Vázquez-Dorrío: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – original draft (equal). Jesús Blanco-García: Investigation (equal); Supervision (equal). José Luis6 Valencia-Álvarez: Investigation (equal); Supervision (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.