Beam qualty measurements wth Shack-Hartmann wavefront sensor and M-sensor: comparson of two methods J.V.Sheldakova, A.V.Kudryashov, V.Y.Zavalova, T.Y.Cherezova* Moscow State Open Unversty, Adaptve Optcs Laboratory Sudostrotelnaya Str 18, Bld. 5, Moscow, Russa 115407 * Department of Physcs, Moscow State Unversty, Vorobyovy Gory, Moscow, Russa 119899 ABSTRACT In both scentfc and ndustral laser beam applcatons s essental for users to know what could be expected from the laser beam. That s why analyss of the laser beam parameters s very mportant durng laser use n varous ndustral and scentfc applcatons. To descrbe the beam one can use a beam qualty factor M that characterzes the degree of mperfecton of a laser beam. There are many methods of beam qualty determnaton. The most common way s to use a devce based on technques descrbed n the Internatonal Standard ISO11146 "Test methods for laser beam parameters: Beam wdths, dvergence angle and beam propagaton factor". For example we can use M-sensor that we desgn and produce n our Lab. The measurement of the beam qualty factor accordng to ISO11146 s not a smple procedure and mght take a long tme. And for some applcatons fast beam qualty determnaton s needed. Moreover sometmes t s not necessary to know the exact value of M, only estmaton of M s just needed. And for the beam qualty estmaton we suggest to use Shack-Hartmann wavefront sensor. Wth ths sensor we can easly and fast measure the wavefront of the beam and then accordng to the wavefront calculate M. The comparson of two sensors s presented. Advantages and dsadvantages are ponted out. Keywords: beam qualty factor M, Shack-Hartmann wavefront sensor, M-sensor 1. INTRODUCTION The measurement of M parameter became very popular because ts value quanttatvely compares the characterstcs of the real beam to those of a pure TEM 00. For the Gaussan beam M = 1. For any other M > 1. The relatonshp between M, wavelength λ, near-feld wast dameter d 0 and dvergence angle θ s 1 : M = π 0θ 4λ d. (1) The dvergence angle s determned as: d f θ =, () f where d s the beam dameter at the focal dstance f of the used lens. So to evaluate M t s necessary to measure both f far-feld beam dameter (to determne dvergence angle) and near-feld one.. DIRECT M MEASUREMENTS WITH M-SENSOR Varous methods of beam qualty determnaton could be suggested 1-4. To measure M a specal sensor based on wellknown technques s usually used. The most common way s to use a devce based on a technque descrbed n the Internatonal Standard ISO11146 "Test methods for laser beam parameters: Beam wdths, dvergence angle and beam propagaton factor" 1. The algorthm of measurements proposed n ISO11146 s based on a fxed-poston lens and
multple beam-wdth measurements made through the focal plane wast (Fg.1). At least 0 measurements have to be taken where half of them should be dstrbuted wthn one Raylegh length on ether sde of the beam wast and half of them should be dstrbuted beyond two Raylegh lengths from the beam wast. The M -factor and dvergence angle could be easly obtaned from performng a hyperbolc ft to the measured beam dameters along the beam propagaton axs: d = A+ Bz + Cz, (3) where d s the beam dameter at the locaton z, A, B, C are the hyperbola parameters. Then the beam propagaton factor can be calculated usng smple equatons 1 : M π = 4 λ AC B / 4. (4) In our Lab we desgned M-sensor 5 to measure M ; the setup s very smple, t conssts of a focusng element and CCD placed on a movng stage (Fg.). The dsadvantage of ths devce and ths technque s that we have to do lots of measurements and some adjustment s needed every tme we move CCD. So ths procedure mght take a long tme. But for some applcatons fast beam qualty determnaton s needed. Moreover sometmes t s not necessary to know the exact value of M, only estmaton of M s just needed. And for the beam qualty estmaton we suggest to use Shack- Hartmann wavefront sensor. Fg. 1. Prncple of M measurements Fg.. Photography of our M-sensor 3. INDIRECT M MEASUREMENTS WITH SHACK-HARTMANN WAVEFRONT SENSOR Wth Shack-Hartmann wavefront sensor we can easly and fast measure the wavefront of the beam 6. The wavefront determnaton by Shack-Hartmann wavefront sensor s based on the measurements of local slopes of a dstorted wavefront ϕ/ n (Fg.3). So, the whole wavefront s dvded n several subapertures by some phase plate or lenslet array and the devaton of the focal spot from some reference poston n each subaperture s measured. Fg. 3 provdes some dea about the work of the sensor. To measure a pattern of focal spots a standard CCD camera s used. We also produce n our Lab Shack-Hartmann Wavefront sensors (Fg.4). Beam reszng lens s used to match the dameter of nput beam and CCD.
Fg. 3. Idea of Shack-Hartmann wavefront sensor Fg. 4. Photography of our Shack-Hartmann wavefront sensor Also from the CCD we have nformaton about beam ntensty. Of course we have only dscrete ntensty dstrbuton and n case of huge ngomogenty of ntensty dstrbuton we cannot obtan correct result but stll f the ntensty s qute smooth we have enough amounts of ponts to reconstruct the ntensty. And f beam phase and ntensty dstrbuton s known we can obtan far feld ntensty dstrbuton I far feld usng FFT and then to calculate M as d( I far feld ) M =. (10) d gauss The advantage of Shack-Hartmann wavefront sensor s that we need only one measurement to obtan M. So n comparson wth M-sensor we have less adjustment. 4. EXAMPLES OF M MEASUREMENTS The results of our experment made n Dusburg-Essen Unversty, Germany (group of Alexander Tarasevtch), n femtosecond T:S laser are presented as an example of M measurement. Here we had 10 Hz pulses wth duraton of 5 fs and output energy of 00 mj. Frst we measured wavefront wth Shack-Hartmann wavefront sensor, P-V was around 1.1 (Fg.5a). Fg.5b shows far feld ntensty dstrbuton calculated wth FFT; for ths dstrbuton M s 3. After that we placed 5 meter focusng lens n order to measure M usng standard procedure descrbed n 1. The focal plane ntensty dstrbuton s presented on Fg.5c. Obtaned M s also 3 n ths case. So n case of sngle mode beam we can successfully use Shack-Hartmann wavefront sensor to measure M.
a b c Fg. 5. T:S laser beam nvestgaton. a wavefront of the beam, b calculated far feld ntensty dstrbuton, с measured far feld ntensty dstrbuton As a next example we present our experment n DSO Natonal Laboratores, Sngapore (group of La Kng Seng). We tred to measure the aberratons of CW Nd:YAG ceramc laser wth output power of 500 W. The output beam had a lot of hgh order modes. Frst we measured wavefront (Fg.6a) of the beam and calculated far feld ntensty dstrbuton. M was around 3 n ths case (Fg.6b). But as soon as we measured far feld wth 100 mm lens we found out that real M s more than 55 (Fg.6c) and ths value has nothng to do wth the one measured wth Shack-Hartmann wavefront sensor. The man reason of ths awful result s that the beam was mult mode one. And as we cannot separate one mode from another we measured some averaged phase wth Shack-Hartmann sensor. That s why the result mght be ncorrect, and the M value s also unpredctable. a b c Fg. 6. Nd: YAG laser beam nvestgaton. a wavefront of the beam, b calculated far feld ntensty dstrbuton, с measured far feld ntensty dstrbuton 5. COMPARISON OF TWO METHODS Table 1 shows the comparson of two sensors: M-sensor and Shack-Hartmann wavefront sensor. The man advantage of Shack-Hartmann wavefront sensor s that we need only one measurement whle usng standard M-sensor we have lots of work to do. Shack-Hartmann wavefront sensor s good for sngle mode and sngle pulse radaton. But unfortunately wth ths sensor we cannot obtan correct results for multmode radaton. And wth M-sensor of course we are able to measure any beam: sngle mode, multmode and CW or wth hgh repetton rate.
Advantages Dsadvantages Table 1. Advantages and dsadvantages of two sensors M-sensor Correct result whle both sngle and multmode beam analyss Convenent for CW or pulse lasers wth hgh repetton rate Slow measurements Shack-Hartmann wavefront sensor Sngle measurement to obtan M value very fast and smple Ablty to analyse sngle mode radaton Very convenent to measure sngle mode sngle pulse laser radaton Unpredctable result whle multmode beam analyss 6. CONCLUSION The possblty of M measurement wth Shack-Hartmann wavefront sensor s shown. The comparson of M-sensor and Shack-Hartmann wavefront sensor s presented. Advantages and dsadvantages are ponted out. But we should be very careful whle mult mode beams analyss. Examples of both sngle-mode and mult-mode radaton analyss are presented. The possblty of Shack-Hartmann wavefront sensor use to measure M of sngle-mode laser beam s shown. The result mght be ncorrect whle mult-mode beam analyss. ACKNOLEGEMENTS Authors thank to Dr. Alexander Tarasevtch from Dusburg-Essen Unversty, Germany, and Dr. La Kn Seng from DSO Natonal Laboratores, Sngapore, for the assstance n the experment. REFERENCES 1. Test method for laser beam parameters: Beam wdth, dvergence angle and beam propagaton factor, Document ISO/DIS 11146, Internatonal Organzaton for Standardzaton, 1996.. T. Jonston, Beam propagaton (M ) measurement made as easy as t gets: the four-cuts method, Appled optcs, 37(1), July 1998. 3. K. Roundy, Propagaton factor quantfes laser beam performance, Laser Focus World, 1, pp.119-1, 1999. 4. B. Eppch, S. Johansson, H. Laabs, H. Weber, Measurng laser beam parameters, phase and spatal coherence usng the Wgner dstrbuton, Proc. SPIE, 3930, pp. 76-86, 000. 5. J.V.Sheldakova, T.Yu.Cherezova, A.Kudryashov, "Low-cost M -sensor for the adaptve optcal system", Proc. SPIE 4493, pp. 85-93, 00. 6. V.Ye.Zavalova, A.V.Kudryashov, "Shack-Hartmann wavefront sensor for laser beam analyss", Proc. SPIE 4493, pp. 77-84, 00.