Toolbox of Fisrt Order Optical System Design

Store what I learn in code

These are the notes after taking the 'First Order Optical System Design' course

https://www.coursera.org/learn/first-order-optical-system-design/home/welcome

Rays and Snell's Laws

Ray Tracing and Lens Analysis

Thick lens

def thick_lens_R(R1, R2, d, n, n0=1): phi=1/R1*(n-n0)+1/R2*(n0-n)+d/n*1/R1*1/R2*(n-n0)**2 return phi

yu Tracer and ABCD Matrices

ABCD Matrix

# basic ABCD Matrix def ABCD(a,b,c,d): return Matrix([[a,b],[c,d]]) # Some specific examples def free_space_matrix(d): return ABCD(1, d, 0, 1) def flat_interface_matrix(n1,n2): return ABCD(1,0,0,n1/n2) def curved_interface_matrix(R, n1, n2): return ABCD(1, 0, (n1-n2)/(R*n2), n1/n2) def curved_mirror_matrix(R): return ABCD(1, 0, -2/R, 1) def thin_lens_matrix(f): return ABCD(1, 0, -1/f, 1)

First-Order Ray Tracing of Multi-Element Systems

Reduced angle variable $$$ \hat u \equiv nu $$$

Reduced refraction equation

$$$ \hat u_k^\prime= \hat u - y_k \Phi_k $$$

def u_hat_out(u_hat_in, y_k, phi_k ): return u_hat_in-y_k*phi_k

Reduced distance variables $$$ \hat d \equiv \frac{d}{n} $$$

Reduced transfer equation $$$ y_{k+1}=y_k+\hat u_k^\prime \hat d_k^\prime $$$

def y_next(y_k, u_hat_out, d_k): return y_k+u_hat_out*d_k

y-u tabular ray tracing

d0=symbols('d0')

ray_tracing_table={ "surface":[0,1,2,3], "phi": [0, 1/8, 0, 1/2], "d": [8.4, 168, 2, 0], "y":[0,np.nan,np.nan,np.nan], "u":[10,np.nan,np.nan,np.nan] } ray_tracing_df=pd.DataFrame(ray_tracing_table) ray_tracing_df

# todo # fill the nan

Properties of the Conjugate Matrix

Conjugate condition

N12==0

def solve_conjugate_condition(matrix): return partial(solve, matrix[1])

Object at front focal plane

N22==0

def solve_object_at_front_focal(matrix): return partial(solve, matrix[3])

Image at rear focal

N11==0

def solve_image_at_rear_focal(matrix): return partial(solve, matrix[0])

Afocal condition

N21==0

def solve_afocal_condition(matrix): return partial(solve, matrix[2])

Relating M & N

…which gives the image location in terms of object distance and elements of M

$$$ d_k^\prime = - \frac{ d_1 A-B}{d_1 C -D} $$$

def solve_image_location(M, object_distance): return -(object_distance*M[0]-M[1])/(object_distance*M[2]-M[3])

optical resonator

def one_full_round_trip_of_optical_resonator(r, d): half_trip= ABCD(1, 0, -2/r, 1)* ABCD(1, d, 0, 1) return half_trip**2