Working Principle of Range Finders – Measuring the Distance Between Points A and B Laser range finders typically use two methods to measure distance: the pulse method and the phase method. Pulse Method for Ranging The process of pulse-based ranging is as follows: the laser emitted by the range finder is reflected by the target object and then received back by the range finder. The instrument simultaneously records the round-trip time of the laser beam. Half of the product of the speed of light and the round-trip time equals the distance between the range finder and the target object. The accuracy of pulse method distance measurement is typically around ±1 meter. Additionally, the blind spot for this type of range finder is usually about 15 meters. Laser ranging is a form of optical wave ranging. If light travels at speed cin the atmosphere and the time required for a round trip between points A and B is t, the distance Dbetween points A and B can be expressed as: D = c × t / 2 where:

· D is the distance between points A and B;

· c is the speed of light in the atmosphere;

· t is the time required for light to make a round trip between A and B.

From the formula above, it can be seen that measuring the distance between A and B essentially involves measuring the propagation time tof light. Depending on the method used to measure this time, laser range finders are generally categorized into two types: pulse-based and phase-based. Phase-Based Laser Range Finder Phase-based laser range finders use radio-frequency bands to modulate the amplitude of the laser beam. They measure the phase shift produced by the modulated light during a round trip along the measuring line and then convert this phase shift into distance based on the wavelength of the modulated light. In other words, the time required for the light to travel the round trip is measured indirectly, as shown in the diagram. Phase-based laser range finders are typically used in high-precision ranging applications. Due to their high accuracy, usually at the millimeter level, and to ensure effective signal reflection while limiting the measured target to a specific point matching the instrument’s precision, these devices are often equipped with reflective mirrors known as cooperative target reflectors. If the angular frequency of the modulated light is ω, and the phase delay generated over the round trip of the distance Dto be measured is φ, the corresponding time tcan be expressed as: t = φ / ω Substituting this relationship into the formula D = c × t / 2, the distance Dcan be expressed as: D = 1/2 × c × t = 1/2 × c × φ / ω = c / (4πf) × (Nπ + Δφ) = c / (4f) × (N + ΔN) = U × (N + ΔN) where:

· φis the total phase delay generated over one round trip along the measuring line.

· ωis the angular frequency of the modulated signal, ω = 2πf.

· Uis the unit length, numerically equal to 1/4 of the modulation wavelength.

· Nis the number of half-wavelengths of the modulation signal contained in the measuring line.

· Δφis the part of the phase delay generated over one round trip that is less than π.

· ΔNis the fractional part of the half-wavelength of the modulation signal contained in the measuring line, ΔN = φ / ω.

Under given modulation and standard atmospheric conditions, the value c / (4πf)is a constant. In this case, distance measurement simplifies to measuring the number of half-wavelengths (N) contained in the measuring line and the fractional part less than a half-wavelength (ΔN)—i.e., measuring Nor φ. Thanks to advancements in modern precision machining technology and radio phase measurement techniques, the measurement of φcan now be achieved with very high accuracy. To measure the phase angle φwhen it is less than π, various methods can be employed. The most commonly used methods are delay phase measurement and digital phase measurement. Currently, most short-range laser range finders adopt the digital phase measurement method to determine φ.