The conventional method for measuring displacement errors in CNC machine tools is static—the machine is stopped for a few seconds at each measurement interval to stabilize before positioning data is acquired. For measurements on small-pitch or long-stroke machine tools, this means a considerable amount of downtime. The same measurement, using continuous synchronous data acquisition, only takes a few minutes. In fact, continuous synchronous data acquisition can measure more points, providing more detail while saving time. For example, if a 5-second stop is required every 25 mm, a 1,250 mm axis length and 5 round trips would take over 50 minutes. Furthermore, static positioning errors are usually caused by geometry, guideways, and structural rigidity. Dynamic positioning errors, which are generally not measured, are caused by servo parameters, resonant frequencies, and acceleration or deceleration. In other words, because the machine tool stops before data acquisition, servo or dynamic errors are missed. Theoretically, trajectory accuracy should be improved using dynamic displacement error tables, not static ones. This is particularly important for mold manufacturers, as they must ensure that the mold cavity perfectly matches the complex geometry composed of multiple surfaces. The interferometer, invented by Michelson in 1881, was later awarded the Nobel Prize in Physics in 1907 for its invention of displacement measurement . The Michelson interferometer used white light as its light source and employed both fixed and movable mirrors. It was used to measure or compare distances by calculating interference fringes. With the invention of the laser, a single-frequency helium-neon laser replaced white light as the light source, and two cornerstone prisms replaced plane mirrors. The single-frequency helium-neon laser beam was split into two beams by a beam splitter; one half passed through a movable cornerstone prism, and the other half was reflected back to a fixed cornerstone prism. The two reflected beams met at the beam splitter upon their return. After precisely aligning all the optical paths, the two meeting beams interfered with each other, producing interference fringes. A small-area photodetector was used to count the fringes. The intensity change in each cycle represented half the wavelength of the movable cornerstone prism's travel. If the wavelength of the laser was known, the travel of the movable cornerstone prism could also be accurately determined. The problem with the single-frequency interferometer was its sensitivity to noise. Therefore, it is impossible to distinguish between electrical noise and gain drift from movement. Dual-frequency interferometers use a dual-frequency helium-neon laser to mix two beams of different frequencies to generate a carrier frequency. Therefore, the distance information carried is in AC wave form rather than DC wave form. The problem with dual-frequency interferometers is the need for bulky permanent magnets and precision optical components to stabilize the laser frequency, maintain polarization, and minimize scattered light returning to the laser resonant cavity. Due to the system's bulkiness and numerous optical components, most machine tools require the machine cover to be opened during measurement. Laser Doppler Calibration System Laser Doppler calibration systems use a laser Doppler displacement meter (LDDM), which combines microwave radar technology, the Doppler effect, and optical heterodyne technology. LDDM employs electro-optic and optical heterodyne processes and a phase demodulator to obtain the position information of a moving cone. LDDM measures displacement by illuminating a mirror with a helium-neon laser beam. As the mirror moves, the frequency of the reflected laser beam changes. Since the phase of the reflected laser beam is proportional to the position of the mirror, the change in position can be measured. For LDDM, polarization and diffused light are not issues, and sophisticated optical systems are not required. Mirrors can be inserted freely into the optical path, and simple reflectors can be used to reflect the laser beam to any angle. How to use a laser Doppler calibration system To calibrate a standard or ball screw, a cutting tool is placed on the shaft, and a motor drives the screw to trigger a position sensor. For example, four position sensors can be used to collect four sets of data per revolution. The position sensor sends a TTL pulse to the PCMCIA card to trigger data acquisition. The key to uninterrupted data acquisition is that the external trigger and data acquisition are synchronized with the TTL trigger pulse, i.e., data is acquired simultaneously. A typical ball screw pitch error measured with four position sensors is 0.2 inches per revolution. Therefore, 20 data points can be measured per inch on screws larger than 20 inches. In this example, thermal expansion error is much smaller than pitch error. To calibrate an axis of a CNC machine tool, the laser head is placed on the machine bed, and a reflector or target is mounted on the spindle. The laser beam is aligned parallel to the spindle, just as in a conventional static laser calibration. However, unlike the usual method of moving forward and then stopping for 5 seconds at a time until reaching the finish line, the spindle is now adjusted to move continuously from the start to the finish line without any stops. The position sensor can be placed on the ball screw or its rotating wheel. A non-contact trigger is fixed to a magnetic base. The trigger's blade is placed on the ball screw's rotating wheel. Each rotation of the wheel sends a trigger signal to the PCMCIA card for data acquisition. Some machine tool trigger signals come from the machine tool's controller or encoder output. [align=center]Schematic diagram of calibrating the ball screw with 4 trigger pulses per rotation[/align] Experimental Procedure A Doppler series laser calibration system with a high data rate PCMCIA interface card and external triggers continuously and synchronously acquires data at a rate of 10,000 data points per second. Atmospheric pressure sensors, air temperature sensors, and material temperature sensors automatically compensate for measurement errors caused by wavelength variations, and the thermal expansion of the material is within the laser system's standards. The LDDM laser head is placed on the work platform, while the reflector is mounted on the spindle of the vertical machining center. A non-contact trigger was fixed to a rod on a magnetic base, while a trigger blade was fixed to a rotating wheel. Data was acquired using a laptop computer with a high-speed PCMCIA card. A special cable connected the output of the LDDM processor to the PCMCIA card, and the trigger's signal was connected to the LDDM processor. In the main menu of the LDDM software, the 2-D time base button was used to set the data acquisition parameters. The data rate, time interval, and external trigger could be selected. The maximum speed was 5 meters per second, and the highest data rate was 10,000 data points per second. The data lifetime from the trigger pulse to displacement readout was less than 100 nanoseconds. In the experiment, two laser heads were placed 4.25 inches (10.8 cm) apart along the Y-axis. Displacement data was first acquired using a conventional static data acquisition method, pausing every 2 inches for a total travel of 18 inches. The maximum error was 0.02 inches, and the backlash was 0.005 inches. Then, with the same settings, displacement data was acquired using a non-stop synchronous external trigger. Data was acquired at 0.2-inch intervals for a total travel of 19 inches, with at least five round trips. Two sets of LDDM displacement data were acquired synchronously without interruption. The angular error can be calculated by dividing the difference between the two displacement errors by the separation distance. The maximum angular error was 8.5 arcseconds. The maximum linear reading error was 0.00012 inches. Compared to statically acquired data, the results of synchronously acquired data are similar but contain more detailed information. Using this displacement data to compensate for machine tool errors yields better results than using conventional statically acquired data. Furthermore, using synchronous data acquisition saves time, especially for measurements on small intervals or large machine tools.