Laser spot measurement using simple devices

Precise characterization of the laser profile and the measurement of its spot size are needed for several scientific, industrial, medical, and instrumental applications.^1,2 For example, this kind of characterization is important in Laser-Induced Breakdown Spectroscopy (LIBS), atomic emission spectroscopy, where the laser focuses to form a plasma, which atomizes samples,³ or Laser-Tissue Soldering (LTS), where a protein solution is thermally denatured and cross-linked to obtain a strong bond between tissues or between tissue and a wound dressing.⁴ 

Another application is related to testing new silicon pixel sensor technology,⁵ where it is desired to activate individual pixels using a narrow and focused laser beam. The laser profile has to be known in advance to avoid clustering (i.e., illuminating several pixels at the same time). Several methods for measuring a Gaussian laser diameter have been developed; for a summary, see Ref. 6.

There are studies for this purpose that use a CMOS-based camera,^7,8 and others are based on a quadrant photodiode,^6,9,10 which is generally used for measuring the position of the beam. There are also alternative methods^11–14 for estimating the diameter of a Gaussian laser beam. The aim of this work is to offer simple automated precise methods that use up-to-date technology to measure the spot profile of a Gaussian laser beam.

Our experimental setup, which uses a Raspberry Pi (small single-board computer) for automation, is explained in detail so that it can be assembled in a standard laboratory. It has comparable precision for measuring beam profiles as ready-made optical devices. We are also able to find the smallest spot size in the focal plane, known as the beam waist.

Three different light sensors—a CMOS webcam, a single photodiode, and an LDR (Light Dependent Resistor)—were used and compared to measure the radius of the laser beam. The use of an LDR in this context is innovative. The performance of the methods and sensors was benchmarked against lasers of two different wavelengths and technologies. In addition, we will show that it is possible to use an LDR sensor to roughly estimate the spot size.

This paper is divided as follows: We first describe in Sec. II the properties and parameters of a Gaussian laser beam. Then, in Sec. III, we outline the general experimental setup and the specifically used light sensors and lasers. In Sec. IV A, we give the results of the laser radius and waistline measurements, as well as the comparison/cross-check between different light sensors and commercial optical devices. Finally, in Sec. V, we discuss our findings and give our conclusions.

There are several types of laser profiles, including Gaussian, multi-mode, tilted, flat top, and irregular beams.² A laser with a Gaussian irradiance profile can be easily modeled with well-known mathematical expressions. Thus, we select this type of beam for testing the performance of the different sensors.

An ideal Gaussian laser beam has a symmetrical irradiation profile around its center, decreasing as the distance from the center increases. The waist of a Gaussian beam, w,¹⁵ also called the radius or spot size, is defined as half the distance across the center of the beam where the irradiance is 1/e² (≈13.5%) of its maximum. This value is ∼2σ of the Gaussian fit (see Fig. 1).

The waist at a distance z is given by

where w₀ is the radius of the minimum possible cross section (beam minimum waist), z₀ is the position of w₀, and z_R is the Rayleigh range, which is defined as the distance from the beam waist to the point where the waist is multiplied by $2$⁠. A scheme of these parameters is shown in Fig. 2. The Rayleigh range is determined by

where λ is the free-space wavelength and n is the refractive index of the medium where the beam propagates through.

At large distances (z ≫ z_R), w increases linearly with z; hence, the beam divergence,¹⁵ θ_d, as seen in Fig. 2, given in radians, can be defined, due to diffraction, as

For this study, the beam radius equation (1) will be used to determine the beam profile. To achieve this, it is necessary to measure the values of the laser spot size as a function of the distance to the sensor, as it moves away from the laser. From these data, it is possible to determine the values of w₀, which presents zero divergence, z_R, and z₀.

To measure the laser beam spot, we have designed the experimental setup as shown in Fig. 3 and tested it, applying different methods, three light sensors, and two lasers.

At the bottom of the setup, there is a micrometer that has a resolution of 0.001 in. or 25.4 μm connected to a stepper motor, which allows a minimum horizontal displacement along the y-axis of 10.10 ± 5.05 μm according to the mechanical configuration of the assembly. On top of this micrometer, there is another one that moves the sensor along the z-axis, which is controlled manually and has a resolution of 10 ± 5 μm. Over the z-axis micrometer, each different light sensor (CMOS, photodiode, and LDR) was placed. The sensor is partially isolated from ambient light using a dark chamber with a hole in the upper part, which lets the laser pass through. Fitting this hole, there is an iris diaphragm¹⁶ to reduce beam aberrations. This iris only lets in the light that passes through the opening, which is regulated approximately to the spot size.

An attenuator (i.e., a rectangular step variable metallic neutral density filter, NDL-25S-4¹⁷) is placed between the laser and the sensor to decrease the intensity of the laser, preventing the saturation of the sensor and keeping the Gaussian profile, especially in the case of the CMOS sensor. The attenuator used has an optical density (OD) that varies from 0.1 to 4 with a tolerance of ±5%, divided into ten steps or positions. The OD indicates the attenuation factor provided by an optical filter, i.e., how much it reduces the optical power of an incident beam. OD is related to the transmission, T, by T = 10^−OD. Therefore, the transmission varies from 0.794 to 0.000 1.

At the top of the setup, the laser is held still using a retort stand. The distance between the laser and sensor is determined for each measurement and explained in Sec. IV.

The stepper motor and the sensors were connected to a Raspberry Pi 3b (i.e., a small, low-cost, single-board computer)^18,19 to control the movement and capture the sensor data. Python programs were also developed to process the data directly on the Raspberry and to obtain the average results. The scripts can be found in the supplementary material.²⁰ 

Three different light sensors [a CMOS (webcam), photodiode, and LDR] were used in this configuration. These sensors are cost-affordable.

The first sensor was a 5 MP webcam,^21–23 which uses CMOS technology. We removed the webcam lens so that we are able to measure the spot size directly, according to the size of the pixels illuminated by the laser, every time a shot was taken. The webcam was configured using the Picamera package²⁴ for the Raspberry Pi camera module using Python. The settings were as follows: 16 µs shutter speed (i.e., exposure time) to reduce movement, 2592 × 1944 image resolution, an analog and digital gain of 1, and ISO = 0 to maximally reduce the noise. The format used for image capture is YUV (Y: intensity and UV: color code), which allows images to be captured without loss of detail and with full resolution (1-byte Y value for each pixel). This configuration allows linear behavior of the camera, avoiding overexposure, saturation, and loss of information, necessary to process the data.^25,26

The second sensor was a single PIN photodiode.²⁷ In this case, to determine the beam radius, the photodiode must be moved step-by-step (e.g., similar to the knife-edge technique²⁸) perpendicular to the beam from a position where the whole beam hits the sensor until the beam is outside the sensitive area. This technique will return a Gaussian cumulative distribution function (CDF) curve.

The third sensor was an LDR or photo-resistance.²⁹ This electronic component decreases the resistance when the light intensity on the sensitive surface increases. Even if it is not a precision device, it is inexpensive, widely available, and a novel approach in this context. Here, we apply the same technique used for the photodiode.

The circuits for the photodiode and the LDR consist of a variable resistance in series with the sensor. These circuits are connected to an analog-to-digital converter (ADC) (i.e., ADS1115), which can be read by the Raspberry Pi, as shown in Fig. 4.

Two different lasers were used for the measurements to benchmark the performance of the methods with different wavelengths and technologies. One was a generic 5 mW green semiconductor laser that gives a Gaussian spot according to the manufacturer. A model similar to this laser is found in Ref. 30. The second one was a red He–Ne gas laser with the power <4 mW.³¹ 

The laser intensity can be controlled in two ways; for both lasers, attenuators are used; however, for the green laser, it is also possible to tune the current to lower its intensity, which is not available for the red laser.

In addition, the wavelength and power of each laser were measured in the laboratory. The green semiconductor laser had a 532 nm wavelength and a maximum power of 5.57 mW. Once the intensity was regulated with current and attenuators, the power became 2.83 μW. This laser was attenuated with the density filter reducing its intensity to 0.1% of the incident beam power to avoid saturating the sensor. The red He–Ne gas laser had a 633 nm wavelength and a power of 0.67 mW.

The green semiconductor laser was used to measure the laser profile and to find the beam minimum waist. Thus, a Gaussian profile was obtained. The red He–Ne gas laser was used to compare the beam radius measurement with the three light sensors. This laser has a very stable spot size with distance. Therefore, the beam minimum waist was not searched for, and only the beam radius was measured. In addition, it was necessary to locate the laser at a larger distance than the green laser to avoid saturating the CMOS sensor.

As a benchmark, the radius and waistline of the green semiconductor laser beam were determined using the CMOS sensor. Next, the beam radius measurements using the red He–Ne gas laser obtained with the CMOS sensor were compared with those of the two other sensors: the photodiode and LDR.

The initial distance from the green semiconductor laser to the CMOS sensor was determined as follows: First, the distance between the laser and sensor, where the area of the beam over the sensor is the smallest (beam waist), was visually searched by moving the laser on the z-axis. The distance from the CMOS sensor to the beam waist was measured with a Vernier as 161.94 ± 0.01 mm. The beam waist was scanned around this distance in a ±5 mm range starting with the minimum distance (156.94 ± 0.01 mm). Then, this minimum distance is considered as the initial position (z = 0 mm).

The CMOS sensor was moved away from the laser in 1 mm steps, obtaining 11 measurements. In each position, ten images or frames were captured and converted to ADC intensity matrices. From these data, the value of the radius in each position was calculated.

To calculate the laser beam radius, the projection of the intensity profile in the x and y axes was made. For each frame, both projections were fitted using the following Gaussian function,

obtaining the parameters a (normalization), b (background off-set), μ (mean), and σ (standard deviation).

The beam radius for each axis is the ten-frame average of 2σ. The associated total error was estimated as $Δtot=(∑iΔi2)/N$⁠, where N is the number of frames and Δ_i is the error for each frame, which is calculated by adding in quadrature the error from the Gaussian fit and the systematic error of 0.5 pixels.

To give the results in units of distance, the number of pixels was multiplied by 1.4 μm, which is the size of each CMOS sensor pixel. In Fig. 5, the first frame taken with the CMOS sensor at z = 6 mm is shown, as an example. The projections of the x and y axes of the spot profile are given, as well as the results obtained from the Gaussian fit.

The average spot radius w_xy is calculated by

where σ_x and σ_y are the average standard deviations of the Gaussian fit in the x and y axes, respectively.

To determine the laser profile parameters, the least-square fitting of the data at different distances along the beamline was made using Eq. (1). The parameters obtained with the fit are w₀, the radius of the minimum possible cross section, z₀, the position of w₀, and z_R, the Rayleigh range. Using these parameters, the laser wavelength can be determined from Eq. (2) and the divergence from Eq. (3).

The results obtained at different distances from the CMOS sensor are shown in Fig. 6 and Fig. 7, for the x-axis, w_x, y-axis, w_y, and average w_xy radius, respectively.

Using the average radius [see Eq. (5)], the beam waistline was calculated to be w_0xy = 22.2 ± 0.6 μm, Rayleigh’s range z_Rxy = 2 894.3 ± 136.1 μm, the divergence $θd=w0zR=7.7±0.4$ mrad, and the wavelength $λ=πw02zR=537.0±38.0$ nm. This estimation of wavelength is in good agreement with an independent measurement in the laboratory, which is 532 nm.

To compare the different sensors, we used a red He–Ne gas laser for estimating the beam radius. In this case, the green laser, which has a smaller spot size (between 20 and 45 μm), was not used since the method applied for the photodiode and LDR has a lower resolution than the CMOS sensor. In order to use the photodiode and LDR, a step-wise procedure is used, which has a minimum horizontal displacement of 10.1 μm along the y-axis, while the pixel size of the CMOS is 1.4 μm. Thus, the red laser, which has a larger spot size, was used. For comparison, it is only necessary to measure the spot on one axis; in this case, we chose the y-axis.

The laser was located 467.15 ± 0.05 mm above the sensor for all three sensors to avoid saturation since this laser’s intensity cannot be regulated. In addition, to prevent saturation of the CMOS, different attenuations were tested. We found that the CMOS did not saturate for a transmission of 1% and 0.1% of the initial laser intensity. For lower attenuations, the profile cannot be correctly fitted by a Gaussian. The LDR showed smaller variations in the spot size, also decreasing according to the attenuation. Contrarily, we found for the photodiode that the spot size is almost constant for the transmission range between 100% and 0.1%. All sensor measurements converge at the attenuator with 0.1% transmission. All sensors reach their threshold at the last attenuator position, where only 0.01% of the incident power is transmitted. At this position, the voltage output is compatible with the background.

The laser spot was measured with the photodiode, using the method explained in Sec. III, regulating the resistance of the circuit (see Fig. 4) to improve the sensitivity. Each set of voltage measurements began with the laser pointing inside the sensor. Then, the sensor was moved stepwise along the y-axis until the laser was outside the sensitive area of the sensor. In each step, ten measurements were made. The resulting data were the average. The points obtained from these measurements follow a Gaussian CDF, as seen in Fig. 8, since the profile of the laser is Gaussian.

Thus, we fit these data using the following corresponding function:

where the parameters to fit are a, the normalization, μ, the Gaussian mean (position where half of the beam spot is inside the sensitive area of the detector), σ, the standard deviation (w_y = 2σ), and b, the off-set from the background.

Figure 8 shows an example of the Gaussian CDF fit and the obtained parameters using the photodiode data with an attenuator that allows a transmission of 1% of the incident power and a resistance of 2.2 kΩ. A different value of the resistance would not affect the spot size; it would only change the error since the amplitude is changed.

In addition, the step distance was varied from 10 to 55 μm using a fixed attenuation. The beam radii obtained along the y-axis are stable since the spot is large enough, and it does not depend, in this distance range, on the precision of the steps.

Then the LDR sensor was used to measure the laser spot with an 11.5 Ω resistance, following the same method that was used for the photodiode. Different measurements were performed varying the series resistance of the circuit. In addition, it was observed that the results obtained with the LDR depend on the resistance of the circuit, varying the sensitivity of the sensor. This does not guarantee a reliable measurement of the spot. Only a rough estimate can be given. This is because the LDR does not have a continuous surface that measures the intensity of the beam; rather, it has a zigzag of the light-sensitive semiconductor material with active and non-active areas. In addition, the LDR’s own resistance can vary up to three orders of magnitude due to changes in the intensity of the laser. We estimate that these factors account for an ∼10% error.

Finally, the laser spot was measured using the CMOS sensor, following the same method described in Sec. IV A. To compare the results of the three sensors, the CMOS values are taken as the standard for comparison. The errors are calculated using Eqs. (7) and (8), where σ is the combined error of Δw_sensor, the error in the beam radius estimation obtained for either the photodiode or LDR, and Δw_CMOS, the error of the CMOS. The difference between measurements of different sensors will be given in terms of the number of standard deviations, n_σ,

The errors include the statistical and systematic uncertainties, which are for the CMOS half the pixel size, that is, 0.7 μm, and for the photodiode and LDR, the horizontal displacement of 5 μm. The systematic error for the LDR also adds the aforementioned factors by which the spot cannot be accurately measured, such as the variation in resistance due to the effects of intensity, resistance tolerance, hysteresis effects, etc. These are estimated to be ∼10% of the measurement.

Table I summarizes the results of all three sensors at 0.1% transmission: the CMOS, photodiode and LDR. Considering the uncertainties, the values obtained with the photodiode and LDR are compatible with that of the CMOS (webcam), less than 0.5 σ difference. Figure 9 shows the corresponding fits for all sensors.

The measurement of the spot with the photodiode can be improved using less attenuation or the average of the measurements with the different attenuators since it was observed that the spot size is almost constant for the transmission range between 100% and 0.1%. For example, if we use the 10% transmission attenuator, the spot value would be 506.4 ± 5.3 μm.

Finally, in Table II we compare the characteristics of our most precise method, using the CMOS camera, with some ready-made optical devices (WinCamD-XHR-1/2 in.,³² CinCam CMOS 1204,³³ and CCD BC106N-VIS³⁴) that are used for measuring beam profiles. Our setup included the Raspberry, the CMOS Picam (OV5647), the rectangular density filter, the optical micrometer (LZ60), and electronic accessories.

Since the pixels in our camera are smaller, we can obtain a shorter minimum beam size that can be measured. We consider that to make a good reading of the beam size, it is necessary to have 15 points (i.e., pixels) to describe the Gaussian width. Thus, the minimum beam size for our device is 21 μm. Moreover, the total active area is smaller than the other devices, thus limiting the maximum size of the beam to be measured. In addition, our covered wavelength range is slightly shorter in the infrared.

We have designed and tested the performance of an automatic setup for measuring the spot radius of laser beams using three different light sensors. Two common profiling techniques were implemented: the imaging technique for the CMOS 2D array and the scanning knife-edge-like technique for the single photodiode and LDR.

This implementation can be easily reproduced in a standard laboratory following the procedure explained here with current technology. Our setup measures beam profiles with the same accuracy as commercial devices. While the minimum measurable beam size is smaller than other pieces of equipment, the wavelength range is slightly shorter in the infrared.

The simplest and the highest precision method for beam profiling was using the CMOS sensor. The error in determining the minimum spot radius is less than 3%, while the error on the waistline position is 1.5%. As a separate cross-check of the method, the wavelength of the laser could be determined with a 1% error. This shows that it is possible to use a low-cost webcam to determine the profile of a laser with good precision.

Our results have fewer uncertainties than those obtained in Ref. 7 where the error of the beam waist is 26% with a CMOS sensor compared to 1% in our case. For the method that uses a photodiode, our errors are similar around 12% for the highest attenuation. However, for a different attenuation, our error can improve to less than 2%.

Nevertheless, this method has also some limitations. Due to the CMOS’s greater sensitivity, the sensor can be saturated, and it can produce blooming with a high-intensity laser, distorting its real profile. This problem can be overcome by using attenuators.

The photodiode using the knife-edge-like technique is the most stable method. It is not affected by the change in laser intensity until the attenuation is very high. Its precision for the spot radius measurement is better than 2% under standard conditions. However, a setup with a stepper that moves the sensor along one axis is needed, and the price of the photodiode is five times more expensive than the CMOS webcam.

We have shown that it is possible to use an LDR for measuring the spot size of a laser, which is a novel approach in this context. Nevertheless, the LDR measurement has a strong dependence on the series resistance of the circuit. In addition, the LDR’s own resistance varies about three orders of magnitude depending on the light intensity. It also has a slow response and does not provide linearity with lighting. This limits its precision to accurately measuring the spot of a laser, having an estimated error of 11%. However, it has high sensitivity and a considerable low cost; thus, it can be used to have an estimate of the spot value.

A limitation for the smallest spot that can be measured with the knife-edge-like technique of the photodiode and LDR measurements is related to the mechanical system for horizontal displacement. Currently, the smallest step is 10.1 μm, while the CMOS grid has a pixel size of 1.4 μm. If the mechanical system is improved, smaller spots could be measured with the photodiode and LDR.

Furthermore, the data collection system for spot determination can be improved by automating the movement in the z-axis. This would increase the speed and precision of the measurement.

The authors gratefully acknowledge the Dirección de Gestión de la Investigación (DGI-PUCP) for funding under Grant No. DGI-2019-3-0044. C.S. acknowledges support from the Peruvian National Council for Science, Technology and Technological Innovation scholarship under Grant No. 236-2015-FONDECyT. We would also wish to thank R. Sanchez from the Applied Optics Group and the Quantum Optics Group for letting us use their lasers and equipment, as well as Y. Coello for the photodiode. We also thank J. A. Guerra for useful discussions and suggestions.

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