Optical shadowgraphy can be another method for the measurement of shock speed in laser produced plasma. Following article can be useful for this purpose.

http://lab.fs.uni-lj.si/kolt/datoteke/osebje/peter_gregorcic/PDF/GREGORCIC_Peter_High_speed_two_frame_shadowgraphy_for_velocity_measurements.pdf

A few approaches:

(1) Most common is time-resolved Schlieren imaging

(2) Interferometry with coherence-domain imaging

(3) Time-resolved/gated acoustic signals with hydrophone (needle hydrophone)

you can read the article

(Mechanism of laser-induced plasma shock wave evolution in air

Zhao Rui1, Liang Zhong-Cheng1, Han Bing2, Zhang Hong-Chao2, Xu Rong-Qing3, Lu Jian2 and Ni Xiao-Wu2

2009 Chin. Phys. Soc. and IOP Publishing Ltd Chinese Physics B, Volume 18, Number 5) with its references

If the plasma / shock front produces a change in polarization or gives you a Kerr effect then you might be able to use a modification of traditional Kerr-effect spectroscopy (OHD-RIKE) or time-resolved polarization imaging? See also work by Dana Dlott - for example - Ultrafast imaging of optical damage dynamics and laser‐produced wave propagation in polymethyl methacrylate

Journal of Applied Physics 64, 2955 (1988); https://doi.org/10.1063/1.341556

Virendra Nath Rai Thank you very much,but I have no optical shadowgraphy .

If You are using 1064nm laser for producing plasma then splitting same laser or converting the splitted laser to second harmonic you can use it as a probe beam for shadography. This probe beam can not pass through the shock. So you can record the shock. You can even delay the probe beam optically and then record the shock shadow.

Dear Wang

Above anser may be useful to you.

Virendra Nath Rai Why the probe beam can not pass through the shock？ Could you explain it in detail ？Thank you

Dear Wang

Density of compressed plasma becomes so high that it becomes opaque for the laser light. It is a shielding effect. It depends on the wavelength of laser.

Dear Xianshuang,

For the record, you don't always or necessarily observe optical breakdown or plasma expansion (and I assume you meant in water) with 1064 nm. It is presumed that you are using a Q-switched Nd:YAG laser, fiber delivered or otherwise optically focused into water with an irradiance roughly > 10^12 W/cm2. In Schlieren imaging or shadowgraphy, you will see broad spectrum light from the plasma (plasma behaves like a blackbody emitter) with the passband only limited by any bandpass filter you may be using in your imaging system, and the resulting shockwave appearing dark because the compressive wavefront refracts the probe beam away from (beyond the numerical aperture of) your imaging system. So it is not that the wavefront is blocking the beam, but rather just exhibiting a refractive index gradient that is in proportion to the local compression.

Hope this helps.

Another approach could be using a hydrophone (pvdf or fiber optic based) that has a bandwidth in the signal space. You can measure the signal at varying distances from the shockwave source to get an idea of the velocity.