Scattered light imaging method (SLIM) for characterization of arbitrary laser beam intensity profiles Kelly C. Jorge,1,2,* Rudimar Riva,2 Nicolau A. S. Rodrigues,2 João M. S. Sakamoto,2 and Marcelo G. Destro2 1
2
Division of Fundamental Sciences, Instituto Tecnológico de Aeronáutica, 50 Praça Marechal Eduardo Gomes—Vila das Acácias, São José dos Campos - São Paulo 12.228-900, Brazil
Division of Photonics, Instituto de Estudos Avançados, 1 Trevo Cel. Av. José A. A. do Amarante, São José dos Campos—São Paulo 12.228-001, Brazil *Corresponding author: [email protected] Received 21 February 2014; revised 14 May 2014; accepted 29 May 2014; posted 2 June 2014 (Doc. ID 206759); published 9 July 2014
A laser beam characterization method is reported, which is applicable to arbitrary and ideal laser beam intensity profiles. This method, called the scattered light imaging method (SLIM), is based on scattered light imaging of a laser beam and provides a complete visualization of it in the region of interest. The method was applied to characterize an arbitrary pedestal-shaped beam and compared with a conventional method (camera scanning). The results we presented show that, for arbitrary beams, it seems much more meaningful to know the intensity profile evolution than to determine an M 2 value. Therefore the SLIM is a powerful tool for a new and more complete type of laser beam characterization. © 2014 Optical Society of America OCIS codes: (140.3295) Laser beam characterization; (110.2970) Image detection systems; (290.0290) Scattering. http://dx.doi.org/10.1364/AO.53.004555
1. Introduction
In laser applications, it is important to know the laser beam’s spatial properties because they directly affect the application quality [1–5]. These properties are usually evaluated using laser beam characterization, which is accomplished by measuring the power, beam waist (minimum beam radius) w0 , and divergence angle θ. The product of w0 and θ defines the laser beam propagation factor (formerly known as the beam quality factor [3]), which is given by M 2 πw0 θ∕λ, where λ is the laser wavelength. However, the laser beam cannot be characterized completely using only the M 2 value [3–7] because 1559-128X/14/204555-10$15.00/0 © 2014 Optical Society of America
M 2 does not provide information about the intensity profile of an arbitrary laser beam. M 2 1 indicates an ideal laser beam, i.e., one having the single-mode TEM00 [3,8,9], which has a Gaussian intensity profile. For a laser beam with M 2 > 1, the beam can be formed by either a highorder mode or a mixture of modes (multimode) [3,10], and its intensity profile presents an arbitrary shape that can be very far from that of an ideal laser beam. According to ISO 11146 [8], M 2 is obtained by measuring the laser beam radius in at least 20 longitudinal positions on the beam propagation path, 10 around the beam waist region, and 10 far from it, which allows one to obtain both w0 and θ. Therefore the conventional methods of measuring M 2, such as camera scanning [11], knife-edge [4], slit [12,13], 10 July 2014 / Vol. 53, No. 20 / APPLIED OPTICS
4555
or pinhole (aperture) [14] methods, follow this standard. These methods are usually slow and laborious because they require movable parts to measure several beam radii in several positions. A number of alternative methods have been developed to provide faster M 2 measurement [7,15–22], allowing real-time estimation. However, they are based on a small number of measurements (approximately 10), taken only around the beam waist, which decreases their accuracy. With this background, we present an alternative method that is not only fast and simple, but also a real-time, single-shot method with high accuracy and high sensitivity. It provides, in addition to M 2 , information about the intensity profile evolution, which makes it a powerful tool for characterizing ideal and arbitrary laser beams. This characterization method, here called the scattered light imaging method (SLIM) [23], was patented by the authors [24] and applied to measure the laser beam quality of a single-mode laser [25]. In the SLIM, the laser beam is focused in a scattering medium, and the transverse scattered light is imaged onto a camera. Under a specific configuration of the imaging optical system, just one lateral image is sufficient to provide a complete view of the longitudinal profile on the propagation axis. This image enables the measurement of a great number of laser beam intensity profiles, depending on the number of pixels of the charge-coupled device (CCD) camera (1000 in our case) in one transverse direction (e.g., the y direction), where each point is the intensity summation of its orthogonal transverse direction (e.g., the x direction). It has been demonstrated that the SLIM can be used to measure the laser beam quality of a single shot of a multimode pulsed laser [25]. The average of M 2 for single pulses was found to be lower than the M 2 value obtained by image averaging. Therefore the second type of M 2 measurement may lead to highly incorrect estimations, mainly for pulsed lasers, when conventional methods are used. In addition, the pulse-to-pulse point beam stability and intensity fluctuations were monitored. In this work, we evaluate the performance of the SLIM for the characterization of a laser beam with an arbitrary intensity profile having a meaningful fraction of its power contained in its wings (a pedestal-shaped beam). We used a Nd:YAG pulsed laser and compared the results with those obtained by a conventional method, the camera scanning method (CSM) [11].
yo
Operation Principle
In the SLIM, the laser beam is propagated along the zo direction and focused in a scattering medium (e.g., a liquid, gas, or solid medium) [24]. In this work, the subscripts “o” and “i” refer to the object and image planes of the imaging optical system, respectively. The light of the beam is scattered in the xo and yo 4556
APPLIED OPTICS / Vol. 53, No. 20 / 10 July 2014
Scattering medium
zo Laser Imaging optical system
yi
xi zi
CCD camera
Fig. 1. Schematic diagram of the SLIM.
directions, which are transverse to the beam. The scattered light of the beam is imaged onto an xdirection detection system consisting of lenses and a CCD camera, as shown in Fig. 1. Therefore, the image [shown in Fig. 2(c)] enables the measurement of several y-direction laser beam intensity profiles I SLIM yi ; zi , where each yi point is a summation of the intensity on the xo direction. In addition, the imaging optical system is defined with the optical axis along the x direction, the vertical plane in the y direction, and the horizontal plane in the z direction. The imaging optical system of the SLIM can be simply depicted by a lens of focal length f and size aperture D, as shown in Fig. 2(a), where do and di are the distances between the lens and the object and image planes, respectively, which are related by [26] 1 1 1 : do di f
(1)
The image in Fig. 2(c) is that of an extended object, which is centered on the origin of the xo yo plane and has a width given by the laser beam width (beam diameter or 2w); Fig. 2(b) shows the extended object, which is a typical frontal laser beam intensity profile obtained by the CSM, I CSM xo ; yo ; zo . In this way, the intensity level measured on each CCD camera pixel located on the yi image plane represents the (a)
Slit
Object plane
Image plane
D yo
zo
yi Aperture
xo
zi
(b)
xi
di
do
2. Scattered Light Imaging Method A.
xo
Lens
(c) yi
yo xo
zi
Fig. 2. (a) Simple imaging optical system using lens of focal length f and aperture size D. (b) Frontal laser beam intensity profile given by ICSM xo ; yo ; zo . (c) Image of scattered laser beam propagating in medium formed by many laser beam intensity profiles I SLIM yi ; zi .
contribution from the scattered light of the laser beam intensity profile for the entire depth of focus of the object plane in the xo direction. The accuracy of the beam width measurement using the SLIM depends on the features of the imaging optical system, primarily the effect of the depth of focus on the image quality. This effect is evaluated all along the beam profile in the x direction using the expression known as the impulse response function, hxi ; yi [27]. This function uses the imaging optical system’s features, which are given by f, D, and the positions do and di . The image plane is fixed at di , whereas the object is defined by a plane number (n), which ranges from −N to N (where 2N is the maximum number of planes). The impulse response function is specified for each of the n planes corresponding to the extended object, which are defined as xo do nΔ, where Δ is the xo increment. The coordinates of the image and object planes are related by xi j − xo MagV j, where MagV is the vertical magnification. In the output (image plane) of the system, because the light is incoherent, the image intensity profile is calculated by the convolution (denoted by the symbol ) between the input signal function Ixo ; yo ; zo (or intensity profile) and the square modulus of the impulse response function [27]. Both of these are estimated using the image coordinates, Ixi ; yi ; zi I o xi ; yi ; zi jhxi ; yi j2 :
(2)
For n 0, one has the imaging condition [Eq. (1)]. However, the object is extended, with a width slightly larger than 2w; therefore it is formed by 2N incoherent input signal functions. These functions are convoluted according to Eq. (2) and then integrated to form the final CCD image, given by Z d NΔ i Ixi ; yi ; zi dxi I con yi ; zi Z
di −NΔ
di NΔ di −NΔ
I o xi ; yi ; zi jhxi ; yi j2 dxi ;
I SLIM
di NΔ
di −NΔ
I o xi ; yi ; zi dxi ;
for 2w ≥ the depth of focus; for 2w < the depth of focus and resolution ≪ 2w:
(4)
where the superscript “int” indicates that Ixo ; yo ; zo is only integrated in the xi direction. In conclusion, I SLIM yi ; zi can be represented using Eqs. (3) or (4) depending on whether the depth of focus has an
(5)
In summary, to use the image obtained by the SLIM to characterize the laser beam, it is necessary to meet some minimal requirements [23]: • The scattering medium should be transparent to the laser wavelength and cause spontaneous and homogenous light scattering. • The scattered light intensity must be higher than the CCD camera’s threshold and lower than its saturation level. • The concentration of the scattering medium must be controlled so that the transmitted light at the end of the cell is greater than the CCD camera threshold. In practice, the attenuation of the beam should be at most 10% along the cell. • The magnification of the imaging optical system should be adjusted to measure in one unique image (filling the entire CCD camera) at least three Rayleigh ranges (zRy πw20y ∕λ, where w0y is the y-direction beam waist). • To represent the image in terms of the integral, I int , it is necessary to use a system with a depth of focus much larger than the laser beam width [4λf ∕2 > 2w, where f ∕ f ∕D]. • The vertical (y) resolution should be adjusted much smaller than the beam width. The beam radius wy z of the SLIM beam intensity profile is estimated by the second moment criterion [3,8], which is given by wy
Z
8 con
2
Division of Fundamental Sciences, Instituto Tecnológico de Aeronáutica, 50 Praça Marechal Eduardo Gomes—Vila das Acácias, São José dos Campos - São Paulo 12.228-900, Brazil
Division of Photonics, Instituto de Estudos Avançados, 1 Trevo Cel. Av. José A. A. do Amarante, São José dos Campos—São Paulo 12.228-001, Brazil *Corresponding author: [email protected] Received 21 February 2014; revised 14 May 2014; accepted 29 May 2014; posted 2 June 2014 (Doc. ID 206759); published 9 July 2014
A laser beam characterization method is reported, which is applicable to arbitrary and ideal laser beam intensity profiles. This method, called the scattered light imaging method (SLIM), is based on scattered light imaging of a laser beam and provides a complete visualization of it in the region of interest. The method was applied to characterize an arbitrary pedestal-shaped beam and compared with a conventional method (camera scanning). The results we presented show that, for arbitrary beams, it seems much more meaningful to know the intensity profile evolution than to determine an M 2 value. Therefore the SLIM is a powerful tool for a new and more complete type of laser beam characterization. © 2014 Optical Society of America OCIS codes: (140.3295) Laser beam characterization; (110.2970) Image detection systems; (290.0290) Scattering. http://dx.doi.org/10.1364/AO.53.004555
1. Introduction
In laser applications, it is important to know the laser beam’s spatial properties because they directly affect the application quality [1–5]. These properties are usually evaluated using laser beam characterization, which is accomplished by measuring the power, beam waist (minimum beam radius) w0 , and divergence angle θ. The product of w0 and θ defines the laser beam propagation factor (formerly known as the beam quality factor [3]), which is given by M 2 πw0 θ∕λ, where λ is the laser wavelength. However, the laser beam cannot be characterized completely using only the M 2 value [3–7] because 1559-128X/14/204555-10$15.00/0 © 2014 Optical Society of America
M 2 does not provide information about the intensity profile of an arbitrary laser beam. M 2 1 indicates an ideal laser beam, i.e., one having the single-mode TEM00 [3,8,9], which has a Gaussian intensity profile. For a laser beam with M 2 > 1, the beam can be formed by either a highorder mode or a mixture of modes (multimode) [3,10], and its intensity profile presents an arbitrary shape that can be very far from that of an ideal laser beam. According to ISO 11146 [8], M 2 is obtained by measuring the laser beam radius in at least 20 longitudinal positions on the beam propagation path, 10 around the beam waist region, and 10 far from it, which allows one to obtain both w0 and θ. Therefore the conventional methods of measuring M 2, such as camera scanning [11], knife-edge [4], slit [12,13], 10 July 2014 / Vol. 53, No. 20 / APPLIED OPTICS
4555
or pinhole (aperture) [14] methods, follow this standard. These methods are usually slow and laborious because they require movable parts to measure several beam radii in several positions. A number of alternative methods have been developed to provide faster M 2 measurement [7,15–22], allowing real-time estimation. However, they are based on a small number of measurements (approximately 10), taken only around the beam waist, which decreases their accuracy. With this background, we present an alternative method that is not only fast and simple, but also a real-time, single-shot method with high accuracy and high sensitivity. It provides, in addition to M 2 , information about the intensity profile evolution, which makes it a powerful tool for characterizing ideal and arbitrary laser beams. This characterization method, here called the scattered light imaging method (SLIM) [23], was patented by the authors [24] and applied to measure the laser beam quality of a single-mode laser [25]. In the SLIM, the laser beam is focused in a scattering medium, and the transverse scattered light is imaged onto a camera. Under a specific configuration of the imaging optical system, just one lateral image is sufficient to provide a complete view of the longitudinal profile on the propagation axis. This image enables the measurement of a great number of laser beam intensity profiles, depending on the number of pixels of the charge-coupled device (CCD) camera (1000 in our case) in one transverse direction (e.g., the y direction), where each point is the intensity summation of its orthogonal transverse direction (e.g., the x direction). It has been demonstrated that the SLIM can be used to measure the laser beam quality of a single shot of a multimode pulsed laser [25]. The average of M 2 for single pulses was found to be lower than the M 2 value obtained by image averaging. Therefore the second type of M 2 measurement may lead to highly incorrect estimations, mainly for pulsed lasers, when conventional methods are used. In addition, the pulse-to-pulse point beam stability and intensity fluctuations were monitored. In this work, we evaluate the performance of the SLIM for the characterization of a laser beam with an arbitrary intensity profile having a meaningful fraction of its power contained in its wings (a pedestal-shaped beam). We used a Nd:YAG pulsed laser and compared the results with those obtained by a conventional method, the camera scanning method (CSM) [11].
yo
Operation Principle
In the SLIM, the laser beam is propagated along the zo direction and focused in a scattering medium (e.g., a liquid, gas, or solid medium) [24]. In this work, the subscripts “o” and “i” refer to the object and image planes of the imaging optical system, respectively. The light of the beam is scattered in the xo and yo 4556
APPLIED OPTICS / Vol. 53, No. 20 / 10 July 2014
Scattering medium
zo Laser Imaging optical system
yi
xi zi
CCD camera
Fig. 1. Schematic diagram of the SLIM.
directions, which are transverse to the beam. The scattered light of the beam is imaged onto an xdirection detection system consisting of lenses and a CCD camera, as shown in Fig. 1. Therefore, the image [shown in Fig. 2(c)] enables the measurement of several y-direction laser beam intensity profiles I SLIM yi ; zi , where each yi point is a summation of the intensity on the xo direction. In addition, the imaging optical system is defined with the optical axis along the x direction, the vertical plane in the y direction, and the horizontal plane in the z direction. The imaging optical system of the SLIM can be simply depicted by a lens of focal length f and size aperture D, as shown in Fig. 2(a), where do and di are the distances between the lens and the object and image planes, respectively, which are related by [26] 1 1 1 : do di f
(1)
The image in Fig. 2(c) is that of an extended object, which is centered on the origin of the xo yo plane and has a width given by the laser beam width (beam diameter or 2w); Fig. 2(b) shows the extended object, which is a typical frontal laser beam intensity profile obtained by the CSM, I CSM xo ; yo ; zo . In this way, the intensity level measured on each CCD camera pixel located on the yi image plane represents the (a)
Slit
Object plane
Image plane
D yo
zo
yi Aperture
xo
zi
(b)
xi
di
do
2. Scattered Light Imaging Method A.
xo
Lens
(c) yi
yo xo
zi
Fig. 2. (a) Simple imaging optical system using lens of focal length f and aperture size D. (b) Frontal laser beam intensity profile given by ICSM xo ; yo ; zo . (c) Image of scattered laser beam propagating in medium formed by many laser beam intensity profiles I SLIM yi ; zi .
contribution from the scattered light of the laser beam intensity profile for the entire depth of focus of the object plane in the xo direction. The accuracy of the beam width measurement using the SLIM depends on the features of the imaging optical system, primarily the effect of the depth of focus on the image quality. This effect is evaluated all along the beam profile in the x direction using the expression known as the impulse response function, hxi ; yi [27]. This function uses the imaging optical system’s features, which are given by f, D, and the positions do and di . The image plane is fixed at di , whereas the object is defined by a plane number (n), which ranges from −N to N (where 2N is the maximum number of planes). The impulse response function is specified for each of the n planes corresponding to the extended object, which are defined as xo do nΔ, where Δ is the xo increment. The coordinates of the image and object planes are related by xi j − xo MagV j, where MagV is the vertical magnification. In the output (image plane) of the system, because the light is incoherent, the image intensity profile is calculated by the convolution (denoted by the symbol ) between the input signal function Ixo ; yo ; zo (or intensity profile) and the square modulus of the impulse response function [27]. Both of these are estimated using the image coordinates, Ixi ; yi ; zi I o xi ; yi ; zi jhxi ; yi j2 :
(2)
For n 0, one has the imaging condition [Eq. (1)]. However, the object is extended, with a width slightly larger than 2w; therefore it is formed by 2N incoherent input signal functions. These functions are convoluted according to Eq. (2) and then integrated to form the final CCD image, given by Z d NΔ i Ixi ; yi ; zi dxi I con yi ; zi Z
di −NΔ
di NΔ di −NΔ
I o xi ; yi ; zi jhxi ; yi j2 dxi ;
I SLIM
di NΔ
di −NΔ
I o xi ; yi ; zi dxi ;
for 2w ≥ the depth of focus; for 2w < the depth of focus and resolution ≪ 2w:
(4)
where the superscript “int” indicates that Ixo ; yo ; zo is only integrated in the xi direction. In conclusion, I SLIM yi ; zi can be represented using Eqs. (3) or (4) depending on whether the depth of focus has an
(5)
In summary, to use the image obtained by the SLIM to characterize the laser beam, it is necessary to meet some minimal requirements [23]: • The scattering medium should be transparent to the laser wavelength and cause spontaneous and homogenous light scattering. • The scattered light intensity must be higher than the CCD camera’s threshold and lower than its saturation level. • The concentration of the scattering medium must be controlled so that the transmitted light at the end of the cell is greater than the CCD camera threshold. In practice, the attenuation of the beam should be at most 10% along the cell. • The magnification of the imaging optical system should be adjusted to measure in one unique image (filling the entire CCD camera) at least three Rayleigh ranges (zRy πw20y ∕λ, where w0y is the y-direction beam waist). • To represent the image in terms of the integral, I int , it is necessary to use a system with a depth of focus much larger than the laser beam width [4λf ∕2 > 2w, where f ∕ f ∕D]. • The vertical (y) resolution should be adjusted much smaller than the beam width. The beam radius wy z of the SLIM beam intensity profile is estimated by the second moment criterion [3,8], which is given by wy
Z
8 con
