Exercise : pulsed laser lighting

The object-image lateral magnification must equal:

where the sign of is negative. The digital application gives:

We note that . The lens is assimilated with a thin lens with a center O, such that the position of object (A) is given by:

That is:

Hence, the object is located at a distance of 1.157 m from the camera.

Spatial resolution is due to the size of the pixel which is projected on the object.

That is:

We have:

The laser power transmitted by the variable coupler is . The illumination produced by the laser in the plane of the object is simply:

We consider the object as Lambertian. The Lo luminance produced by the object illuminated by the laser is [1] :

Hence, we have:

Taking into account the cube transmission and the imaging optics, illumination is calculated as follows:

According to the results of the Case Study, for a pixel with a surface px xpy the number of photo-electrons generated by the incident illumination during a length of time equal to the laser pulse and for a wavelength , is:

With the parameters of the previous solution, the following result is obtained:

According to the curve of figure 3, for we have .

The solution can be found using the previous reasoning. The illumination produced on the sensor by the reference beam is:

The number of photo-electrons is thus :

In order for to be true, we obtain the minimum laser energy for the object-beam:

and for the reference beam:

The calculation uses the data from table 5. The transmission of the variable coupler is chosen at . This way, only 10 to 13% of the laser energy is sent to the reference beam.

Table 5: Laser energy calculation [zoom...]

We can observe that the energy required to produce photo-electrons is markedly higher on the object path than that calculated on the reference path. This result is logical. Indeed, the reference beam impacts the sensor directly, whereas the object beam is scattered/diffused by the object toward the sensor. This means that if we were to actually obtain for both beams, then the reference path would have to be even more reduced, by a value in the order of 5x10-5%.

Also note that when working with a less open lens, the required laser energy is considerable: more than 1 kJ in situation 3.

If situation 1 is considered acceptable and the laser is rated at 50Hz then the average power of the laser will be in the order of 488mW of the object of 300mm of diameter. This generates a significant cost to the laser source. If the object is smaller, the laser power will be weaker and the cost lower. The required laser energy may be lowered by increasing pixel size. However, this will be at the detriment of spatial resolution on the object.

An estimate of the maximum acquisition rate of the image sensor can be carried out. The CDD sensor comprises M xN  = 1024x1360 pixels and the pixel frequency is 20 MHz. Therefore, we obtain:

The laser rate (30 Hz à 60 Hz) and the sensor rate do not allow us to study the vibration in real time. Hence, we can only study stationary objects, i.e. objects excited with a frequency that is constant in time. Therefore, we must synchronize with the object and record the images stroboscopically. We realize the following: since the minimum sensor exposure time is 5µs, the sensor must be triggered with a laser pulse chosen within the firing sequence. The laser pulse itself will occur slightly later than the vibration excitation signal of the object. By recording a sequence of laser pulses out of phase with the vibration and covering a vibration period, we can infer the amplitude and the phase of the mechanical vibration.