Log July-12,13

Added method to implement Rayleigh-Sommerfeld-Integral

Rayleigh-Sommerfeld Integral

An Integral used to describe the diffraction of light or sound due to many elements constituting an aperture. It gives an almost perfect computation of the radiation pattern on a focal plane parallel to the plane containing the aperture.

This was implemented using numerical integration for which methods were added as described in the previous blog updates. Commits :
https://github.com/1sand0s/Inter_Haptics/commit/f3906572f6b16c480b077876c63229709fdcc289
https://github.com/1sand0s/Inter_Haptics/commit/510f6eb473ac843306457f3733aae660758457f3
https://github.com/1sand0s/Inter_Haptics/commit/63f35e8796455f3c0062ba6b91fd8f24cd834530
https://github.com/1sand0s/Inter_Haptics/commit/fec3a1f23676d6b4be849bd96bcc25bf4b4303b2
https://github.com/1sand0s/Inter_Haptics/commit/ed79f4899421979e73afc24fcabf56cc7563ae3d
https://github.com/1sand0s/Inter_Haptics/commit/3a59992edf890a414d39dea202b9ed5324bc659e
 deal with their implementation.

The integral models the transducer taking into account everything right from attenuation to frequency.

LOG - July 11

Today was basically spent on updating the code with other important and vital features .

Features Include:

Near Field Length: 

Method was added to compute the near field length. This is very essential since, ultrasonic waves emitted by transducers show uniform properties and attain maximum sound pressure level just beyond the near field length. Before this due to the intense proximity of the wavelets they tend to interfere among themselves and hence give distorted output,and so any tactile sensation must be programmed to be felt so that they are just beyond this length. Commit: https://github.com/1sand0s/Inter_Haptics/commit/559bcb16a5258592e04fbd6828d752f1a7da8074

 deals with this implementation.

As shown in the diagram , in the nearfield the amplitude variations are very abrupt in contrast with the far field variation.

Diffraction Angle

Added diffraction angle measurement for beam emitted by  a single transducer. This helps in accommodating different  transducers with ease if the need should arise. Commit : https://github.com/1sand0s/Inter_Haptics/commit/9aaf565e007dde547cf4e44d4292e8fb55db4057

deals with this implementation 

Sound Pressure and Acoustic Force 

Added method to dynamically calculate the sound pressure and acoustic force on the canvas at the point where the mouse is currently positioned and display it on the canvas. This helps in speculating and designing the type of array best suited for achieving different results like either a rectangular grid array or an annular array etc. Commit https://github.com/1sand0s/Inter_Haptics/commit/28b4c295b3e49f1143cd5d54c8dfb892dc23a88e 

deals with this implementation 

LOG - JULY 10th

Read up on the concepts required for the grid implementation. Added numerical integration to the code. Depending on the step count( number of terms) ,performance and accuracy required the code chooses the most optimum one suited for the purpose at hand.
Commits :  
https://github.com/1sand0s/Inter_Haptics/commit/4ca5fc5fa3a42b2df267d63afdb12ae493753a8d

https://github.com/1sand0s/Inter_Haptics/commit/21a998d8a289d498250cdefc8a246337c202283f
https://github.com/1sand0s/Inter_Haptics/commit/a376edc34eba6c12e5221f51c961500a49fb9460
https://github.com/1sand0s/Inter_Haptics/commit/df8e8b1934c8a1d35cca3725ecaf0ea32dd19c91
https://github.com/1sand0s/Inter_Haptics/commit/5fcde6edbbdfcc91d971327491c737f68cb3baa2
https://github.com/1sand0s/Inter_Haptics/commit/a32fce3c4039d0c463e4642bed9623e1358ec654
https://github.com/1sand0s/Inter_Haptics/commit/613f5d4eeb456abb177ffc86a86171d8d9f2887a
https://github.com/1sand0s/Inter_Haptics/commit/fed2b1f5e62a7c86255268efdf07172f2989c63d
https://github.com/1sand0s/Inter_Haptics/commit/134642b76b7277b0738c0c12c3dfde3724b49680

deal with the implementation of the numerical integration .

1. Trapezoidal 

     Best suited for small step counts and generally when the stress is on performance rather

     than accuracy. Approximates the function curve using trapezoids.

2. Simpson's 1/3

    Best suited when the step count is even. Greater accuracy than that computed using trapezoidal.

    Approximates the function curve using quadratic polynomials(parabolas).

3. Simpson's 3/8

     Best suited when the step count is multiple of 3. Greater accuracy than that of trapezoidal.

     Approximates the function curve using cubic polynomials.

Trial -1

I tested the circuit today. However , though the transmitters are working and the circuit is executing as it is designed to, no perceivable Haptic sensation was felt.

Possible Reasons

These are some of the possible reasons that might provide a plausible explanation for the failure.

1. I was unable to procure the MAX44250 20V opamp as earlier described , and hence had to resort 

    to the one I had in possession which was 741- 12 V opamp. Therefore since the murata MA40S4S 

    datasheet states the max voltage to be around 20V(peak to peak) for the transmitters, it might be

    possible  that the voltage after amplification fed to the transmitters, being of 12 V range was 

    insufficient for them to emit waves of SPL(sound pressure level)of required amplitude to be felt.

2. Secondly, the present algorithm is designed to calculate phase delays for a line of transmitters

    rather than for a grid and since atleast 16 transmitters are required for the amplitude pertaining to

    the constructive interference to be large enough to be felt, this was nearly impossible to achieve          
     using a line of 16 transmitters ,since as stated by the murata MA40S4S datasheet,they have a 

    directivity of about 60 degrees and hence get heavily damped towards the lateral direction ,

    therefore by the time the wave from the 16th transmitter reaches the first ,its barely strong enough

    to complement to the interference.

Possible Solutions

1. Firstly , replace the present 741 12V opamp with MAX44250 20V opamp and hence increase the      
    supply voltage to the transmitters.

2. Secondly, implement the algorithm for a grid of transmitters thereby cutting short the distance

    each wave has to travel to the point of convergence thereby ensuring the amplitude does not get 

    damped heavily. 

Circuit :-

555-Timers

We use two 555's to generate the 40KHz square wave and 200Hz square wave, the 40khz is required to excite the transmitter with its resonant frequency of oscillation and 200hz to modulate the 40khz wave so that our hands can feel the pressure point. 

                So basically Tlow for the first 555 producing 200hz is= 1/(2*200hz)=2.5 ms

so 2.5ms=0.69*R1*C, choosing C as 0.1uf, R1=36k ohms approx.In order to get symmetric wave the charging and the discharging time constant of the capacitor should be the same therefore R1=R2=36k ohms, and during charging from 5v source ,both R1 and R2 is in path of C, therefore we bypass R1 with a diode , now the during charging ,C charges only through R2 since the diode acting as short bypasses R1. 

                The same goes for The second 555 timer, except here Tlow =1/(2*40khz)=12.5us,so 

12.5us=0.69*R1*C, choosing C as 0.1uf, R1=180 ohms approx.

AD633

The square wave outputs from the two 555's are then fed into the inputs of AD633 analog multiplier ,which amplitude modulates the two waves, meaning, the amplitude of the carrier(40khz) is modulated with the 200hz wave.

MAX44250

This is an high precision,low noise,minimal dc offset 20V rail-rail op-amp with bandwidth of about 10Mhz well above the required 40Khz. The timers produce an output wave of 5Vp, we need to amplify this to about 20Vp in-order to attain maximum sound pressure level from the transmitters, therefore for non-inverting config 

                                              1+(Rf/Ri)=Vout/Vin, Vin=5Vp,Vout=20Vp,

Therefore 1+(Rf/Ri)=4,or Rf/Ri=3, therefore choosing Rf as 3K ohm and Ri as 1k ohm, we obtain the desired gain.

Clamper

Although the wave is alternating, yet it has a peak voltage of 20V rather than a peak-peak voltage of 20V with peak voltage of 10v, therefore we employ a clamping circuit to increase the negative dc bias, in other words we shift the positive 20V peak ,10V below ,so that we have 10V peak symmetric wave with 20Vp-p

where 'V' is 10V,

BJT Switch

The output from the clamper ,is then fed to the transmitter via a bjt switch monitored by the digital pins of the arduino. When the digital pins are high, they forward bias the p-n junction between the base and emitter respectively therefore allowing collector voltage to reach the emitter or the transmitters.

Finished Circuit, haven't included the base and collector resistance for the transistor due to lack of
clarity, however they must be added or else the 5v supply from the digital pins of arduino will fry the transistors

Simulation Of Transmitters and Phase Delay Calculations

Pardon me , sir for keeping you in the dark for all this time but i needed to get something conclusive before submitting the results. I have completed coding the simulation for the ultrasonic transmitters which is also capable of calculating the phase delay for n number of transmitters (as of now limited to linear ,array not yet implemented) and also capable of transmitting this data to an arduino(still have to figure out the character encoding and flushing the serial buffer but the code is complete). The link to the code is https://github.com/1sand0s/Inter_Haptics/tree/master/IS_UltraSonic/src/IS_UltraSonic.

The link to the video showing the implementation is below:-
https://youtu.be/lzrv-VvoatU

As shown in the diagram , in order to change the directivity or the angle of the principle maximum ,the transmitters are excited at different instances thereby causing constructive interference at different points and hence changing the orientation of the maximum. Lx is the distance from the transmitter at nth position to the focal point and R is the distance from the central transmitter , so Lx is compared with R and the transmitter is either set back or advanced by a factor ((mod(Lx-R))/speed) and this phase delay results in a constructive interference at the desired point.

Material Read In First Week Of June

Through the various papers referred , i have inferred the following points

Transmission: 
 As specified before , i intended to use the 40khz ultrasonic transmitter  from murata-MA40S4S 
 (i have ordered in bulk after it perfectly suited the need for the project with the favorable directivity and sound pressure level) .For the sake of clarity i recapitulate ,they basically contain quartz crystals which undergo deformation upon application of an AC wave and if the frequency of the applied AC wave coincides with the resonant frequency of the crystal ,the amplitude of the output mechanical disturbance(ultrasonic wave) is maximum .However tiny receptors embedded in our skin called mechanoreceptors

are incapable of detecting vibrations at a frequency of 40khz, it is most sensitive in the frequency range

Therefore i plan to modulate the AC 40khz sinusoid with the amplitude of a 100-200 Hz sinusoid and hence creating a multi-frequency wave which is then amplified to 15Vp-p and fed to the transmitter

Focal Points
This is what i am focusing right now on, reading up material on phase-plane and basically try to correlate the points of constructive interference to the phase differences of the transmitter to form the focal point and eliminate the background noise