**Best answer by David Nguyen**

# Output radius of the CPC in the Merit Function

Yes, we do !

The maths behind the CPC objects are described in the Help File. Retrieving the output diameter implies solving a quadratic equation with the CPC parameters.

This sort of tasks is usually addressed through user defined operands that are written with the Zemax Programming Language (ZPL). As described in this knowledge base article.

I’m attaching the ZPL Macro to this thread, and I’ve also copied it here for your reference.

# Constants

PI = 3.14159265359

# CPC object number from Hx cell of ZPLM

cpc_number = PVHX()

# === Retrieve CPC parameters === #

# Radial aperture

aper = NPAR(1, cpc_number, 1)

# Angle (deg)

t = NPAR(1, cpc_number, 2)

# Angle (rad)

t = t/180*PI

# Volume index

is_vol = NPAR(1, cpc_number, 6)

nd = NPAR(1, cpc_number, 7)

# Refracted angle (rad)

IF (nd > 1)

IF (is_vol > 0)

t = ASIN(SINE(t)/nd)

ENDIF

ENDIF

# Length

L = NPAR(1, cpc_number, 3)

# =============================== #

# === Definitions from CPC Help file === #

C = COSI(t)

S = SINE(t)

P = 1+S

Q = 1+P

T = 1+Q

# ====================================== #

# Maximum length of the CPC

L_max = aper*(1+S)*C/(S*S)

# If current length is longer than maximum length

# change it to the maximum length

IF (L > L_max) THEN (L = L_max)

# Resolution of the quadratic equation for the

# output radius

A_coeff = C*C

B_coeff = 2*(C*S*L+aper*P*P)

C_coeff = (L*L*S*S-2*aper*C*Q*L-aper*aper*P*T)

delta = SQRT(B_coeff*B_coeff-4*A_coeff*C_coeff)

# Physically meaningful solution

Output_radius = (-B_coeff+delta)/(2*A_coeff)

# Return to Merit Function

OPTRETURN 0, Output_radius

This macro should be placed in the \Documents\Zemax\Macros folder, and can be called in the Merit Function through the ZPLM operand where Mac# is 2, and Hx corresponds to the CPC Object number in the non-sequential component editor.

The result looks as follow for a default CPC:

This operand can then be constrained with the OPGT and OPLT operands.

When I try to use the macro, I get the error: *Divide by zero error on line 42. *Do you have any insight as to why/how I can remedy this?

Thanks!

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