Assalamualaikum. The limits 14 % to 86 % are incorrect. Rather, the curve is an error function which is an intregration of the Gaussian. For 14 % to 86 % I have calculated that a multiplicative factor of 0.926 is required. 16 % to 84 % requires multiplicative factor of ~ 1. i.e. the rise time multiplied by 1 gives waist radius in time. You then have to multiply by the 2*pi*r*f. I also wish to mention this video was great. Helped me loads. Saved my time. God bless you!
Well since your chopper wheel frequency isn't constant you will have to calculate the waist size at each position "by hand". the value of "r" is the distance from the center of the hopper wheel to where the beam hits the wheel near the edge. This is used to find the linear velocity of the chopper teeth as they cross the beam, given the angular velocity of the chopper wheel (found from its rotation frequency). The linear velocity unnecessary to convert the rise time as the teeth cross the beam into a distance corresponding to the beam diameter.
The tool in the eBook will calculate the beam size at each point where you measured the beam using your timing data, however it assumes the chopper frequency is constant and uses the same frequency to calculate the beam width at each data point. When I said "by hand" I meant you will have to calculate the beam width at each data point yourself using the appropriate chopper frequency at each point. You can still use the tool to do a curve fit of the data to get w0 and z0. Just set the measurement mode to "generic" instead of "chopper" and enter your processed data for beam width instead of your raw data for rise time.
Sorry may I ask you about the variable resistance that you were using in the end part of the video? Do you have any link or something that may help me to find something like that? Your reply is really appreciated. Thank you.
It is a 1MΩ potentiometer inside of a box. One terminal is connected to the BNC ground, and the wiper is connected to the pin of the BNC connector. This provides a variable resistance from the BNC pin to ground. A T-connector allows this to be put in parallel with the oscilloscope's input.
its pretty simple calculations. check out www.cvilaseroptics.com/file/general/All_About_Gaussian_Beam_OpticsWEB.pdf for a really good explanation and the equations
sorry! May i Ask something i didnt understood? I want to find the beam waist size "Wo" of the beam the location of the waist "z" ok i have the choppe and the PHdetector and i am taking measure for 5 different 'z" and i measure th W for each "z" Ihave problem ..for example for the first measurement .. . If i have z= 15 cm and f =23 Hz and Δt=1.3 ms how i find the W for this location "z" ? do you have any formula for W ? i have not understand good ... *ps i have your e-learn book and i sent you friend request at facebook (Manos Arxontakis)
There is a formula that you can use, but if you have the eBook check out interactive widget 4.1 and set the measurement mode to "chopper" it will let you type in the values you measured and it will calculate wo and zo for you. Basically, in addition to what you told me you need to know the N number of teeth on the chopper wheel, T the period of the waveform you measure on the oscilloscope and Δt its rise time (ideally from the 16.7% power point to the 83.7% power point although you can use other values if you include a numerical correction factor). The ratio of the rise time to the period is the same as the ratio of the beam diameter to the period of the chopper teeth found from the r radial position of the spot on the chopper wheel (2πr/N). Then the Gaussian beam radius is found from that ratio (2ω)/(2πr/N)=Δt/T. Solve this for ω(z)=(π r Δt)/(T N), where for every value of z, you should measure a different value of Δt (but all other parameters remain fixed).
Μανος Αρχοντάκης Hallo and sorry again! 1) the period of the wavefront on the oscilloscope for each different location of the wheel is not the same for me for example my chopper wheel in the lab does not have constant frequency (i have for example 30 Hz at the controller of the wheel and it plays from 30 to 31 or 32 all the time) and 2) what you define "r" the distance of the beam spot on the teeth to the center of the wheel ?
Assalamualaikum. The limits 14 % to 86 % are incorrect. Rather, the curve is an error function which is an intregration of the Gaussian. For 14 % to 86 % I have calculated that a multiplicative factor of 0.926 is required. 16 % to 84 % requires multiplicative factor of ~ 1. i.e. the rise time multiplied by 1 gives waist radius in time. You then have to multiply by the 2*pi*r*f.
I also wish to mention this video was great. Helped me loads. Saved my time. God bless you!
please share us the equations and the calculations... at least in the description...
Well since your chopper wheel frequency isn't constant you will have to calculate the waist size at each position "by hand". the value of "r" is the distance from the center of the hopper wheel to where the beam hits the wheel near the edge. This is used to find the linear velocity of the chopper teeth as they cross the beam, given the angular velocity of the chopper wheel (found from its rotation frequency). The linear velocity unnecessary to convert the rise time as the teeth cross the beam into a distance corresponding to the beam diameter.
what do you mean by hand;
The tool in the eBook will calculate the beam size at each point where you measured the beam using your timing data, however it assumes the chopper frequency is constant and uses the same frequency to calculate the beam width at each data point. When I said "by hand" I meant you will have to calculate the beam width at each data point yourself using the appropriate chopper frequency at each point. You can still use the tool to do a curve fit of the data to get w0 and z0. Just set the measurement mode to "generic" instead of "chopper" and enter your processed data for beam width instead of your raw data for rise time.
Sorry may I ask you about the variable resistance that you were using in the end part of the video? Do you have any link or something that may help me to find something like that? Your reply is really appreciated. Thank you.
It is a 1MΩ potentiometer inside of a box. One terminal is connected to the BNC ground, and the wiper is connected to the pin of the BNC connector. This provides a variable resistance from the BNC pin to ground. A T-connector allows this to be put in parallel with the oscilloscope's input.
If you measure the beam diameters after the lens, how do you back calculate the beam diameter hitting the lens ?
its pretty simple calculations. check out www.cvilaseroptics.com/file/general/All_About_Gaussian_Beam_OpticsWEB.pdf for a really good explanation and the equations
very useful, thanks
sorry! May i Ask something i didnt understood?
I want to find the beam waist size "Wo" of the beam the location of the waist "z"
ok i have the choppe and the PHdetector and i am taking measure for 5 different 'z" and i measure th W for each "z"
Ihave problem ..for example for the first measurement .. . If i have z= 15 cm and f =23 Hz and Δt=1.3 ms how i find the W for this location "z" ? do you have any formula for W ?
i have not understand good ...
*ps i have your e-learn book and i sent you friend request at facebook (Manos Arxontakis)
There is a formula that you can use, but if you have the eBook check out interactive widget 4.1 and set the measurement mode to "chopper" it will let you type in the values you measured and it will calculate wo and zo for you. Basically, in addition to what you told me you need to know the N number of teeth on the chopper wheel, T the period of the waveform you measure on the oscilloscope and Δt its rise time (ideally from the 16.7% power point to the 83.7% power point although you can use other values if you include a numerical correction factor). The ratio of the rise time to the period is the same as the ratio of the beam diameter to the period of the chopper teeth found from the r radial position of the spot on the chopper wheel (2πr/N). Then the Gaussian beam radius is found from that ratio (2ω)/(2πr/N)=Δt/T. Solve this for ω(z)=(π r Δt)/(T N), where for every value of z, you should measure a different value of Δt (but all other parameters remain fixed).
Peter Beyersdorf super!
thanks a lot Mr Peter!
Μανος Αρχοντάκης Hallo and sorry again! 1) the period of the wavefront on the oscilloscope for each different location of the wheel is not the same for me for example my chopper wheel in the lab does not have constant frequency (i have for example 30 Hz at the controller of the wheel and it plays from 30 to 31 or 32 all the time) and 2) what you define "r" the distance of the beam spot on the teeth to the center of the wheel ?