TECHNICAL NOTE

Coherence length of single laserpulses as measured by CCD interferometry

Vladimyros Devrelis, Martin O’Connor, and Jesper Munch

Anovel interferometric method for the direct, real-timemeasurement of the complete temporal coherencefunction of a pulsed laser is presented. AMichelson interferometer is modified by replacing one mirrorwith an inclined diffraction grating to observe interference fringes as a function of path-length differenceon a single pulse. Computerized data acquisition and methods of extending the range of wavelengths tothe infrared are discussed.Key words: Coherence length, interferometry.

1. Introduction

In some experiments it is necessary to measure thecomplete coherence function of a single laser pulse.Until now, the only method available was the holo-graphic approach we discussed in Ref. 1. In thatapproach, a hologram of an inclined plane is recordedwith the laser to be diagnosed. When the resultinghologram is reconstructed, the intensity distributionof the resulting image of the inclined plane can beused to determine the complete coherence propertiesof the single laser pulse. Although this methodworks well, it is limited to parts of the spectrumwhere holographic emulsions function, and it is notconvenient, real time, or suitable for modern experi-ments in which lasers operate at high-pulse-repeti-tion rateswith computerized data-acquisition systems.In this Note we discuss a novel approach that solves

all the limitations of the holographic method whileretaining the fundamental measurement capability.As we show, the new method is an interferometricmethod that records in digital form the direct interfer-ence fringes for all path-length differences on a singlelaser pulse, as well as the transverse intensity distri-butions of the individual interfering beams.Although the optical layout has many similaritieswith the holographic method of Ref. 1, the newmethod differs significantly in its direct measurementof the fringe visibility as opposed to the holographicmethod, in which the coherence function was re-

The authors are with the Department of Physics and Mathemati-cal Physics, University of Adelaide, Adelaide, South Australia,Australia 5005.Received 26 July 1994; revised manuscript received 3 April 1995.0003-6935@95@245386-04$06.00@0.

r 1995 Optical Society of America.

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trieved from the brightness distribution of the recon-structed image.The present interferometer was developed as a

diagnostic instrument for experiments on optical phaseconjugation by the use of stimulated Brillouin scatter-ing. The experiments are a continuation of thosedescribed in Ref. 2, which at that time led to thedevelopment of the holographic approach. The pres-ent experiments investigate the effect of intermediatecoherence lengths on simulated Brillouin scatteringwith a pulsed Nd:YAG laser operating at 1.06 µm anda pulse-repetition rate of 10 Hz. At this wavelength,conventional holograms are difficult to make. Fur-thermore, for intermediate values, the coherencelength is rarely exactly reproduced from pulse topulse, because of the weak axial mode control used.We thus need a new, convenient method to measurethe complete coherence function for each laser pulseat infrared wavelengths, and the present methodsatisfies all these requirements. There are othermethods for measuring coherence length, includingthe original Michelson approach,3 etalons,4 and phaseconjugate interferometers.5 None of these methodscan yield the complete coherence function on a singlelaser pulse, and they are only suited for use on cwlasers where path lengths or etalon spacings can bescanned as a function of time. An additional methodoften used for single pulses is the temporal pulseshape, but this method is not reliable, as discussed inRef. 1.

2. Approach

The temporal coherence function of a source is usu-ally determined from an observation of the visibilityof the interference fringes formed as a function ofpath-length difference when two parts of the source

are made to interfere with each other.4 Thus, for twobeams of intensity I1 and I2 interfering with eachother with a path-length difference l, the normalizedinterference pattern IN1l2 can yield the visibility V1l2and hence the mutual coherence function of the twobeams, g121l2, from

IN1l2 5I1 1 I2 1 2g121l2ŒI1I2 cos kx

I1 1 I25 1 1 V1l2cos kx,

with

V1l2 52g121l2ŒI1I2I1 1 I2

,

where all intensities are functions of the transversecoordinates 1x, y2 and k describes the interferencepattern in one dimension 1fringes are parallel to the yaxis in this case2.This measurement is usually done for a continuous

source by measurement of V1l2, I1, and I2 for differentvalues of l in a Michelson interferometer. The chal-lenge for a pulsed source is to include all possiblevalues of l in a single pulse. This was accomplishedin the holographic method by using a diffuse inclinedplane. In an interferometer we need an inclinedspecular reflector of good optical quality to producerecognizable interferometric fringes. Small strips ofmirror placed at different values of l could be used toproduce a discontinuous sample of the coherencefunction. We chose a better method, making use of ablazed diffraction grating in a Littrow mount. Thegrating is a high-quality optical element that canproduce interference fringes that are observable witha CCD camera.The concept is illustrated in Fig. 1, which shows a

Michelson interferometer with the inclined grating inone arm. There is a line on the grating marked D forwhich the path lengths of the interferometer arms

Fig. 1. Michelson interferometer with a blazed diffraction gratingas one of the reflectors. The optical path lengths AB and AD areequal. Interference produced from lines E and F corresponds toshorter and longer path-length differences, respectively. B.S.,beam splitter.

are equal. Excellent fringe visibility will result fromlight reflected from this part of the grating. Lightfrom other parts 1E and F2 on the inclined grating willtake shorter or longer times to reach the interferenceplane on the CCD camera. The visibility of theinterference fringes from these parts will thereforedepend on the coherence length of the laser. Theinstantaneous, complete coherence function can thusbe observed as the visibility of the fringes along thegrating as seen on the TV monitor for each pulse.This direct observation of the coherence function isespecially useful when one is adjusting intracavityetalons in the laser resonator to produce intermediatecoherence lengths. When permanent data are re-quired, the computer can grab and store the fringepattern. When appropriate masks are used to coverparts of the reflectors, independent measurements ofslices of the intensity distribution of each of theinterfering beams together with the interferencepattern can be obtained on a single frame. Cross-

Fig. 2. Typical interference patterns observed on the TV monitor:1a2 long coherence length, 1b2 short coherence length. The hori-zontal center line on each figure corresponds to path-matched inter-ference. Above the center line corresponds to shorter paths 1regionE in Fig. 12, and below the center line corresponds to longer paths.

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sectional intensity profiles of the interfering beamsand the interference pattern are obtained from col-umns of the digitized frame, and from these data thecomplete coherence function can be calculated.The grating used was 210 mm long, with 600

lines@mm, and blazed at 17°. We needed an inclinedplane as long as possible along the beam and madeuse of the fact that for the 90° groove shape often usedon gratings, the diffraction efficiency is high at boththe blaze angle and its complement. The gratingwas thus reversed and used with an angle of incidenceof 73°, as shown in Fig. 1. A telescope was used toexpand the beam to fill the grating. The closest andfurthest points on the grating along the direction ofthe laser beam were separated by 200 mm, allowingcoherence lengths of up to 400 mm to be measuredwith the setup shown.

3. Results

Typical examples of long- 1injection-seeded2 and short-1no axial mode control2 coherence-length fringe pat-terns are shown in Fig. 2. The uneven intensitydistribution is due to transverse variations in theintensity of the two interfering beams, I11x, y2 andI21x, y2. By recording I1 and I2 separately, one canstill obtain the mutual coherence function g121l2 asdiscussed above. This unevenness, together withthe high contrast of Fig. 2, tends to mask the envelopeof the interference fringes used for real-time observa-

Fig. 3. Plot of the normalized intensity distribution obtainedfrom a single column of the digitized frame showing the resultingfringe visibility as a function of path-length difference along thegrating for the interferograms shown in Fig. 2. 1a2 long coherencelength, 1b2 short coherence length.

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tion of the coherence length, but on a TV monitor, itwas readily observable. Plots of the normalized inter-ference pattern, 1 1 V1l2cos kx, for the data shown inFig. 2 are shown in Fig. 3. In Fig. 3 the envelope ofthe interference pattern is the mutual coherencefunction, and the coherence length is defined as thepath-length difference required for reduction of thevisibility by a factor of 2 as compared with thepath-matched condition.3,4 From Fig. 3 the coher-ence length of the multimode pulse can be seen to be17 mm, and the coherence length of the injection-seeded pulse exceeded the maximum length measur-able 1.0.4 m2. In a separate experiment the longcoherence length was determined to be 3 m 1seebelow2. The noise and the lack of symmetry of thefringes shown are believed to be the result of imperfec-tions in the normalizing procedure and variations inthe intensity from pulse to pulse. For our purposes,this is not considered a limitation and can be im-proved by recording all intensities required on eachpulse, as suggested above, and by improving thestatistics by averaging adjacent pixel columns.The coherence length measurable in the system

shown is limited by the length of the grating. Thislimitation can easily be overcome by additional refer-ence mirrors arranged in such a way as to createnarrow slices of the grating, each slice representingfurther samples of path-length difference, as shown inFig. 4. These slices can form a continuous coherencefunction by separating the mirrors by the gratinglength as shown or can yield piecemeal samples in thecase of very long 1e.g., 3 m2 coherence lengths.

4. Concluding Remarks

Using components found in most modern optics labo-ratories, we have assembled and demonstrated asimple diagnostic tool that can record the completecoherence function of a single laser pulse. Themethod permits real-time observations of the wholevisibility pattern and is capable of producing near-real-time coherence functions, which are limited by the

Fig. 4. Experimental arrangement with multiple reference mir-rors 1M1, M2, M32, used to extend the effective range of thecoherence lengthsmeasurablewith a single grating. For a continu-ous coherence function, the separation of the mirrors should be L,the length of the grating along the beam.

speed and the capacity of the computer frame grabber.The method is useful over the whole range of visibleand infrared wavelengths in which CCD cameras andother imaging arrays function.

This work was supported in part by research grantsfrom the Australian Research Council and the De-fence Science Technology Organization.

References and Notes1. R. F. Wuerker, J. Munch, and L. O. Heflinger, ‘‘Coherence

length measured directly by holography,’’ Appl. Opt. 28, 1015–1017 119892.

2. J. Munch, R. F. Wuerker, and M. J. LeFebvre, ‘‘Interactionlength for optical phase conjugation by SBS,’’ Appl. Opt. 28,3099–3105 119892.

3. A. A. Michelson, Studies in Optics 1U. Chicago Press, Chicago,19272, pp. 34–45.

4. For an excellent review, see A. S. Marathery, Elements ofOptical Coherence Theory 1Wiley, New York, 19872, Chap. 5, orW. Koechner, Solid-State Laser Engineering, 3rd ed. 1Springer,NewYork, 19922, section 5.2

5. C. Bhan, K. Syam Sundara Rao, and P. C. Mehta, ‘‘Measure-ment of the coherence length of a laser using a holographicallygenerated phase-conjugate wavefront,’’ Appl. Opt. 30, 4282–4283 119912.

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