Please check my observations about AN5894

[TGrod]

Are formulas 1-4 correct in AN5894?

Segment [AC] is the hypotenuse of triangle ACE, and the angle between segments [AC] and [CE] is half the dihedral angle HFOV. Then formula 1 should have a sine instead of a tangent.

If I am right, in the example the angle between the segment [CB] and the opposite segment of the pyramid should be [DFoV] = 2*ASin(Sqrt(2*(Sin(60/2))^2)/Sqrt((Sin(60/2) )^2+1)) = 78.5 degrees. This value agrees with measurements made on the 3D model.

[Anne BIGOT]

Hello,

To do our calculation we took the ABC triangle for which we have :

 

The hypotenuse is in this case the segment [BC] and this is the example taken in the AN.

Regards

Anne

[TGrod]

Thank you for your answer.

Then HFOV is not a dihedral angle but the angle of a lateral face of a pyramid at its apex – between its lateral edges.

Please confirm if I am correct.

[Anne BIGOT]

You are correct. The HFOV is the angle of a lateral face and AC is the altitude of the face.

[TGrod]

Can you also explain Figure 1 and Table 2 from the VL53L7CH datasheet?

Using the formulas from AN5894, for a 74 degree angle the diagonal should be 93.4 not 105. The value of 105 is approximately sqrt(2) greater than 74.

[Anne BIGOT]

Using formula 4 from AN5894, the dFOV for a 74 degrees angle should be 116° and not 105°. 

Figure 1 is the same figure as the one of the AN5894 with two different squares : one is 60x60 and the other one 74x74

The table 2 gives the results of equation 4 for a 60° square and a 74° square. Angles are the ones of the triangle at the top of the pyramid. 

[TGrod]

Thank you. My miscalculation.
So let's move further.

How Figure 1 correspond to Figure 27 of VL53L7CH datasheet?

If exclusion zone pyramid has HFoV of 74 degrees (116.66 diagonal) then the dihedral angle of this pyramid should be 2x angle between [AC] and [EC] = 2*asin([EA]/[AC]); [EA] = [AC]*tan(HFoV/2).
So this angle should be 2*asin(tan(74/2)) = 97.8 degrees, but Figure 27 gives 72.5.

Maybe I'm interpreting something incorrectly?

[John E KVAM]

I'm thinking you are confusing the exclusion zone with the effective field of view. 

The VCSEL sends full power in a region of 60 x 60 degrees. But it doesn't go to zero at the edges. There is a rolloff.

If you put a structure in the exclusion zone (rolloff area), even 25% of the light hitting something close up will cause an issue. 

We had hours of argument all around putting the effective FoV in the model or putting in the exclusion zone. 

We assumed most people would use this model to design their structure. So, we went with the exclusion zone. 

But you are using it to model your FoV. 

The FoV is 60x60 - more or less. If your target is close and very reflective, it can be detected even wider than the 60 degrees would suggest. And if your target were dull and far away, you'd probably have to move in a bit less than the 60 degrees before you were guaranteed a detection. It all depends on the number of photons returning from your target. 

[TGrod]

I'm aware that the given angle values for field of view should be treated as approximate.
But the calculations for the exclusion zone (which should probably be precise) with the values in Figure 1, Table 2 and Figure 27 do not match, or I interpret them incorrectly.