# Neutrino detector lens design

# I. Single Hamamatsu multi-anode 8x8 array detector

2003.11.12

Want to have largest possible acceptance angle and image the spots onto
a 52x52mm square detector with 8x8 pixel array. Each pixel is on a 6 mm
pitch grid.

Basic starting parameters:

## 3 field angles: 0°, 20°, 45°

Effective focal length must be 25 mm to image extreme field onto
detector.

Object space medium is WATER. Interior space is AIR.

Start with basic paraxial system. The field rays are coming in from
infinity on the left. The first surface is a dummy set 50 mm infront of
the aperture stop. The field rays fill the aperture stop. The lens is 50
mm to the left of the apeture stop. The rays are refracted from this
ideal lens and directed to the ideal focus positions in the image plane.
It never gets this good in real life.

![](media/image1.wmf){width="3.0in" height="2.25in"}

Now put in a real lens with BK7 glass. Eventually need a glass with good
400nm transmission. Close down the aperture stop and open it slowly
while optimizing the lens with a effective focal length of 25 mm.
Constraining the focal length does not work well in keeping the image on
the detector. Use the CENY (centroid y-value) operand later.

Weight the on-axis field 10 times more than the others. A 20 mm aperture
diameter is about the max we can do before we lose rays.

Aperture stop position is in front of first lens surface.

### 1Lens.zmx

![](media/image2.wmf){width="3.0in" height="2.25in"}

Now put a 4^th^ order even asphere onto both lens surfaces. The image
improves immediately.

![](media/image3.wmf){width="3.0in" height="2.25in"}

Increase the aperture to 29 mm dia before losing it:

![](media/image4.wmf){width="3.0in" height="2.25in"}

Add 6^th^ order asphere term, can go up to 32 mm dia. This is is about
the best we can do with a single lens.

![](media/image5.wmf){width="3.0in" height="2.25in"}

Now go back to spherical surfaces and add a second lens.

## 2 Lens design -- add a second lens

### 2Lens.zmx

Can get to 28 mm entrance aperture diameter before things get too bad.
Both lenses are BK7.

![](media/image6.wmf){width="3.0in" height="2.25in"}

Increase to 32 mm the 2 Lens design:

![](media/image7.wmf){width="3.0in" height="2.25in"}

# 2003.11.13

Two lens design continued. No asphere. Using EFFL = 25 mm as constraint
on image size.

Look in Ohara, Schott, and Hoya glass catalogs for UV-transmissive
glass. Hoya LAC14 looks good. N=1.71 at 400nm.

Can go up to aperture of 34 mm, but outer spots are pretty bad.

### 2Lens02.zmx

![](media/image8.wmf){width="3.0in" height="2.25in"}

Back to 1Lens Asphere design. Put in real LAC14 glass.

Can get the aperture up to 40 mm.

### 1Lens Asph02.zmx

![](media/image9.wmf){width="3.0in" height="2.25in"}

Now expand field angle to add a 55° field. Can only get to 33 mm
aperture.

However, the EFFL operand fails to keep max field position at 25 mm for
aspheric surfaces. Need to go to CENY after this run.

![](media/image10.wmf){width="3.0in" height="2.25in"}

## Go back to 1 Lens design.

Start with plane parallel surfaces, Field angle max at 45°, aperture at
30mm. Then add conic to back, then to front. Up the aperture to 32mm.

### 1Lens Asph02conic.zmx

![](media/image11.wmf){width="3.0in" height="2.25in"}

Increasing the aperture from 32 to 34 mm makes the image deteriorate
rapidly:

![](media/image12.wmf){width="3.0in" height="2.25in"}

So with a single lens, the best we can do is a 32 mm aperture to keep
the spot sizes less than 3 mm rms diameter. Optimize for 25 mm image
size:

### 1Lens Asph02conic2.zmx

![](media/image13.wmf){width="3.0in" height="2.25in"}

# II. Increase image plane to 104x104 mm.

Use 2x2 array of Hamamatsu 8x8 element detector. Can get wider field
angle coverage because lenses don't have to work as hard to put image in
small area.

## Now increase max field to 72°.

Aperture max is about 28 mm before losing it. Fields are now equally
spaced at 18° intervals: 0,18,36, 54 and 72°.

![](media/image14.wmf){width="3.0in" height="2.25in"}

**2 Lens Spherical with stop between lenses**.

Best we can do is 30mm aperture and 54° field.

B2Lens sph.zmx

![](media/image15.wmf){width="3.0in" height="2.25in"}

Put stop between 2 lenses. Put conics on 2^nd^ lens.Best we can do is
48mm aperture, but see that the incident ray bundle for the 54° field is
much smaller diameter than the others. Can only get out to 54° field
angle, even with conics on 2^nd^ lens.

B2Lens conic midstop.zmx

![](media/image16.wmf){width="3.0in" height="2.25in"}

### 2 Lens Spherical with stop in front of lens.

Put stop in front of first element. Start with small aperture and 45°
max field. Increase field angle and aperture size until spots get big.

These are all spherical elements. Max aperture is 40 mm, max field is
65°.

![](media/image17.wmf){width="3.0in" height="2.25in"}

### 2 Lens Conic

Now add conics to each surface in the above design. Not too much
improvement.

![](media/image18.wmf){width="3.0in" height="2.25in"}

### 2 Lens Conic asphere

Add odd asphere to both elements, all 4 surfaces, to see if spot size
can be reduced at margins. Need to reduce aperture to 35mm to make it
work. Not to much better than conic alone.

![](media/image19.wmf){width="3.0in" height="2.25in"}