o o hQ@sNdZgdZddlmZddlmZmZddlmZddl m Z m Z ddl m Z ddlmZdd lmZmZdd lmZdd lmZGd d d eZGdddeZGdddeZGdddeZGdddeZGdddeZGdddeZGdddeZGdddeZd,dd Z d!d"Z!d#d$Z"d%d&Z#e#Z$d'd(Z%d)d*Z&d+S)-a Gaussian optics. The module implements: - Ray transfer matrices for geometrical and gaussian optics. See RayTransferMatrix, GeometricRay and BeamParameter - Conjugation relations for geometrical and gaussian optics. See geometric_conj*, gauss_conj and conjugate_gauss_beams The conventions for the distances are as follows: focal distance positive for convergent lenses object distance positive for real objects image distance positive for real images )RayTransferMatrix FreeSpaceFlatRefractionCurvedRefraction FlatMirror CurvedMirrorThinLens GeometricRay BeamParameterwaist2rayleighrayleigh2waistgeometric_conj_abgeometric_conj_afgeometric_conj_bf gaussian_conjconjugate_gauss_beams)Expr)Ipi)sympify)imre)sqrt)atan2)MatrixMutableDenseMatrix)together) filldedentc@sPeZdZdZddZddZeddZedd Zed d Z ed d Z dS)ra Base class for a Ray Transfer Matrix. It should be used if there is not already a more specific subclass mentioned in See Also. Parameters ========== parameters : A, B, C and D or 2x2 matrix (Matrix(2, 2, [A, B, C, D])) Examples ======== >>> from sympy.physics.optics import RayTransferMatrix, ThinLens >>> from sympy import Symbol, Matrix >>> mat = RayTransferMatrix(1, 2, 3, 4) >>> mat Matrix([ [1, 2], [3, 4]]) >>> RayTransferMatrix(Matrix([[1, 2], [3, 4]])) Matrix([ [1, 2], [3, 4]]) >>> mat.A 1 >>> f = Symbol('f') >>> lens = ThinLens(f) >>> lens Matrix([ [ 1, 0], [-1/f, 1]]) >>> lens.C -1/f See Also ======== GeometricRay, BeamParameter, FreeSpace, FlatRefraction, CurvedRefraction, FlatMirror, CurvedMirror, ThinLens References ========== .. [1] https://en.wikipedia.org/wiki/Ray_transfer_matrix_analysis cGst|dkr|d|df|d|dff}n#t|dkr0t|dtr0|djdkr0|d}n ttdt|t||S)Nr)r r z` Expecting 2x2 Matrix or the 4 elements of the Matrix but got %slen isinstancershape ValueErrorrstr__new__clsargstempr-q/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/physics/optics/gaussopt.pyr(ss "    zRayTransferMatrix.__new__cCst|trtt|t|St|trtt|t|St|trKt|t|jfdf}|d|djdd}t|jtt |tt |dSt ||S)NrrrT)complex)z_r) r$rrrr qexpandwavelenrrr__mul__)selfotherr,r2r-r-r.r5s      zRayTransferMatrix.__mul__cC|dS)z The A parameter of the Matrix. Examples ======== >>> from sympy.physics.optics import RayTransferMatrix >>> mat = RayTransferMatrix(1, 2, 3, 4) >>> mat.A 1 )rrr-r6r-r-r.A zRayTransferMatrix.AcCr8)z The B parameter of the Matrix. Examples ======== >>> from sympy.physics.optics import RayTransferMatrix >>> mat = RayTransferMatrix(1, 2, 3, 4) >>> mat.B 2 )rrr-r9r-r-r.Br;zRayTransferMatrix.BcCr8)z The C parameter of the Matrix. Examples ======== >>> from sympy.physics.optics import RayTransferMatrix >>> mat = RayTransferMatrix(1, 2, 3, 4) >>> mat.C 3 )rrr-r9r-r-r.Cr;zRayTransferMatrix.CcCr8)z The D parameter of the Matrix. Examples ======== >>> from sympy.physics.optics import RayTransferMatrix >>> mat = RayTransferMatrix(1, 2, 3, 4) >>> mat.D 4 )rrr-r9r-r-r.Dr;zRayTransferMatrix.DN) __name__ __module__ __qualname____doc__r(r5propertyr:r<r=r>r-r-r-r.r;s7   rc@eZdZdZddZdS)raQ Ray Transfer Matrix for free space. Parameters ========== distance See Also ======== RayTransferMatrix Examples ======== >>> from sympy.physics.optics import FreeSpace >>> from sympy import symbols >>> d = symbols('d') >>> FreeSpace(d) Matrix([ [1, d], [0, 1]]) cCst|d|ddSNrrrr()r*dr-r-r.r(zFreeSpace.__new__Nr?r@rArBr(r-r-r-r.r rc@rD)ra Ray Transfer Matrix for refraction. Parameters ========== n1 : Refractive index of one medium. n2 : Refractive index of other medium. See Also ======== RayTransferMatrix Examples ======== >>> from sympy.physics.optics import FlatRefraction >>> from sympy import symbols >>> n1, n2 = symbols('n1 n2') >>> FlatRefraction(n1, n2) Matrix([ [1, 0], [0, n1/n2]]) cCs(tt||f\}}t|ddd||SrEmaprrr()r*n1n2r-r-r.r(szFlatRefraction.__new__NrIr-r-r-r.rs rc@rD)raB Ray Transfer Matrix for refraction on curved interface. Parameters ========== R : Radius of curvature (positive for concave). n1 : Refractive index of one medium. n2 : Refractive index of other medium. See Also ======== RayTransferMatrix Examples ======== >>> from sympy.physics.optics import CurvedRefraction >>> from sympy import symbols >>> R, n1, n2 = symbols('R n1 n2') >>> CurvedRefraction(R, n1, n2) Matrix([ [ 1, 0], [(n1 - n2)/(R*n2), n1/n2]]) cCs8tt|||f\}}}t|dd||||||SrErK)r*RrMrNr-r-r.r((s"zCurvedRefraction.__new__NrIr-r-r-r.r s rc@rD)rz Ray Transfer Matrix for reflection. See Also ======== RayTransferMatrix Examples ======== >>> from sympy.physics.optics import FlatMirror >>> FlatMirror() Matrix([ [1, 0], [0, 1]]) cCst|ddddSrErF)r*r-r-r.r(?rHzFlatMirror.__new__NrIr-r-r-r.r-s rc@rD)ra Ray Transfer Matrix for reflection from curved surface. Parameters ========== R : radius of curvature (positive for concave) See Also ======== RayTransferMatrix Examples ======== >>> from sympy.physics.optics import CurvedMirror >>> from sympy import symbols >>> R = symbols('R') >>> CurvedMirror(R) Matrix([ [ 1, 0], [-2/R, 1]]) cCt|}t|ddd|dS)Nrrrrr()r*rOr-r-r.r(\zCurvedMirror.__new__NrIr-r-r-r.rCrJrc@rD)ram Ray Transfer Matrix for a thin lens. Parameters ========== f : The focal distance. See Also ======== RayTransferMatrix Examples ======== >>> from sympy.physics.optics import ThinLens >>> from sympy import symbols >>> f = symbols('f') >>> ThinLens(f) Matrix([ [ 1, 0], [-1/f, 1]]) cCrP)NrrrR)r*fr-r-r.r({rSzThinLens.__new__NrIr-r-r-r.ras rc@s0eZdZdZddZeddZeddZdS) ra Representation for a geometric ray in the Ray Transfer Matrix formalism. Parameters ========== h : height, and angle : angle, or matrix : a 2x1 matrix (Matrix(2, 1, [height, angle])) Examples ======== >>> from sympy.physics.optics import GeometricRay, FreeSpace >>> from sympy import symbols, Matrix >>> d, h, angle = symbols('d, h, angle') >>> GeometricRay(h, angle) Matrix([ [ h], [angle]]) >>> FreeSpace(d)*GeometricRay(h, angle) Matrix([ [angle*d + h], [ angle]]) >>> GeometricRay( Matrix( ((h,), (angle,)) ) ) Matrix([ [ h], [angle]]) See Also ======== RayTransferMatrix cGstt|dkrt|dtr|djdkr|d}nt|dkr*|df|dff}n ttdt|t||S)Nrr)r rr z` Expecting 2x1 Matrix or the 2 elements of the Matrix but got %sr"r)r-r-r.r(s   zGeometricRay.__new__cCr8)a0 The distance from the optical axis. Examples ======== >>> from sympy.physics.optics import GeometricRay >>> from sympy import symbols >>> h, angle = symbols('h, angle') >>> gRay = GeometricRay(h, angle) >>> gRay.height h rr-r9r-r-r.heightzGeometricRay.heightcCr8)a0 The angle with the optical axis. Examples ======== >>> from sympy.physics.optics import GeometricRay >>> from sympy import symbols >>> h, angle = symbols('h, angle') >>> gRay = GeometricRay(h, angle) >>> gRay.angle angle rr-r9r-r-r.anglerWzGeometricRay.angleN)r?r@rArBr(rCrVrXr-r-r-r.rs' rc@seZdZdZdddZeddZedd Zed d Zed d Z eddZ eddZ eddZ eddZ eddZeddZeddZdS)r a Representation for a gaussian ray in the Ray Transfer Matrix formalism. Parameters ========== wavelen : the wavelength, z : the distance to waist, and w : the waist, or z_r : the rayleigh range. n : the refractive index of medium. Examples ======== >>> from sympy.physics.optics import BeamParameter >>> p = BeamParameter(530e-9, 1, w=1e-3) >>> p.q 1 + 1.88679245283019*I*pi >>> p.q.n() 1.0 + 5.92753330865999*I >>> p.w_0.n() 0.00100000000000000 >>> p.z_r.n() 5.92753330865999 >>> from sympy.physics.optics import FreeSpace >>> fs = FreeSpace(10) >>> p1 = fs*p >>> p.w.n() 0.00101413072159615 >>> p1.w.n() 0.00210803120913829 See Also ======== RayTransferMatrix References ========== .. [1] https://en.wikipedia.org/wiki/Complex_beam_parameter .. [2] https://en.wikipedia.org/wiki/Gaussian_beam NrcCs~t|}t|}t|}|dur|durt|}n|dur*|dur*tt|||}n |dur6|dur6tdt|||||S)NzMust specify one of w and z_r.)rr r&rr()r*r4zr1wnr-r-r.r(s zBeamParameter.__new__cC |jdS)Nrr+r9r-r-r.r4  zBeamParameter.wavelencCr\)Nrr]r9r-r-r.rY$r^zBeamParameter.zcCr\)Nr r]r9r-r-r.r1(r^zBeamParameter.z_rcCr\)Nr!r]r9r-r-r.r[,r^zBeamParameter.ncCs|jt|jS)a The complex parameter representing the beam. Examples ======== >>> from sympy.physics.optics import BeamParameter >>> p = BeamParameter(530e-9, 1, w=1e-3) >>> p.q 1 + 1.88679245283019*I*pi )rYrr1r9r-r-r.r20 zBeamParameter.qcCs|jd|j|jdS)a The radius of curvature of the phase front. Examples ======== >>> from sympy.physics.optics import BeamParameter >>> p = BeamParameter(530e-9, 1, w=1e-3) >>> p.radius 1 + 3.55998576005696*pi**2 rr )rYr1r9r-r-r.radius?s zBeamParameter.radiuscCs|jtd|j|jdS)a The radius of the beam w(z), at any position z along the beam. The beam radius at `1/e^2` intensity (axial value). See Also ======== w_0 : The minimal radius of beam. Examples ======== >>> from sympy.physics.optics import BeamParameter >>> p = BeamParameter(530e-9, 1, w=1e-3) >>> p.w 0.001*sqrt(0.2809/pi**2 + 1) rr )w_0rrYr1r9r-r-r.rZNszBeamParameter.wcCst|jt|j|jS)ar The minimal radius of beam at `1/e^2` intensity (peak value). See Also ======== w : the beam radius at `1/e^2` intensity (axial value). Examples ======== >>> from sympy.physics.optics import BeamParameter >>> p = BeamParameter(530e-9, 1, w=1e-3) >>> p.w_0 0.00100000000000000 )rr1rr[r4r9r-r-r.radszBeamParameter.w_0cCs|jt|jS)z Half of the total angular spread. Examples ======== >>> from sympy.physics.optics import BeamParameter >>> p = BeamParameter(530e-9, 1, w=1e-3) >>> p.divergence 0.00053/pi )r4rrar9r-r-r. divergencexr_zBeamParameter.divergencecCst|j|jS)z The Gouy phase. Examples ======== >>> from sympy.physics.optics import BeamParameter >>> p = BeamParameter(530e-9, 1, w=1e-3) >>> p.gouy atan(0.53/pi) )rrYr1r9r-r-r.gouys zBeamParameter.gouycCsd|jtS)a The minimal waist for which the gauss beam approximation is valid. Explanation =========== The gauss beam is a solution to the paraxial equation. For curvatures that are too great it is not a valid approximation. Examples ======== >>> from sympy.physics.optics import BeamParameter >>> p = BeamParameter(530e-9, 1, w=1e-3) >>> p.waist_approximation_limit 1.06e-6/pi r )r4rr9r-r-r.waist_approximation_limitsz'BeamParameter.waist_approximation_limit)NNr)r?r@rArBr(rCr4rYr1r[r2r`rZrarbrcrdr-r-r-r.r s2 2          r rcCs&tt||f\}}|d|t|S)a^ Calculate the rayleigh range from the waist of a gaussian beam. See Also ======== rayleigh2waist, BeamParameter Examples ======== >>> from sympy.physics.optics import waist2rayleigh >>> from sympy import symbols >>> w, wavelen = symbols('w wavelen') >>> waist2rayleigh(w, wavelen) pi*w**2/wavelen r )rLrr)rZr4r[r-r-r.r sr cCs"tt||f\}}t|t|S)ajCalculate the waist from the rayleigh range of a gaussian beam. See Also ======== waist2rayleigh, BeamParameter Examples ======== >>> from sympy.physics.optics import rayleigh2waist >>> from sympy import symbols >>> z_r, wavelen = symbols('z_r wavelen') >>> rayleigh2waist(z_r, wavelen) sqrt(wavelen*z_r)/sqrt(pi) )rLrrr)r1r4r-r-r.r sr cCs<tt||f\}}|js|jr|jr|S|S||||S)a Conjugation relation for geometrical beams under paraxial conditions. Explanation =========== Takes the distances to the optical element and returns the needed focal distance. See Also ======== geometric_conj_af, geometric_conj_bf Examples ======== >>> from sympy.physics.optics import geometric_conj_ab >>> from sympy import symbols >>> a, b = symbols('a b') >>> geometric_conj_ab(a, b) a*b/(a + b) )rLr is_infinite)abr-r-r.r s r cCs tt||f\}}t||  S)a Conjugation relation for geometrical beams under paraxial conditions. Explanation =========== Takes the object distance (for geometric_conj_af) or the image distance (for geometric_conj_bf) to the optical element and the focal distance. Then it returns the other distance needed for conjugation. See Also ======== geometric_conj_ab Examples ======== >>> from sympy.physics.optics.gaussopt import geometric_conj_af, geometric_conj_bf >>> from sympy import symbols >>> a, b, f = symbols('a b f') >>> geometric_conj_af(a, f) a*f/(a - f) >>> geometric_conj_bf(b, f) b*f/(b - f) )rLrr )rfrUr-r-r.r sr cCstt|||f\}}}dd||d||d|}dtd||d||d}|d||d||d}|||fS)a Conjugation relation for gaussian beams. Parameters ========== s_in : The distance to optical element from the waist. z_r_in : The rayleigh range of the incident beam. f : The focal length of the optical element. Returns ======= a tuple containing (s_out, z_r_out, m) s_out : The distance between the new waist and the optical element. z_r_out : The rayleigh range of the emergent beam. m : The ration between the new and the old waists. Examples ======== >>> from sympy.physics.optics import gaussian_conj >>> from sympy import symbols >>> s_in, z_r_in, f = symbols('s_in z_r_in f') >>> gaussian_conj(s_in, z_r_in, f)[0] 1/(-1/(s_in + z_r_in**2/(-f + s_in)) + 1/f) >>> gaussian_conj(s_in, z_r_in, f)[1] z_r_in/(1 - s_in**2/f**2 + z_r_in**2/f**2) >>> gaussian_conj(s_in, z_r_in, f)[2] 1/sqrt(1 - s_in**2/f**2 + z_r_in**2/f**2) rrTr )rLrr)s_inz_r_inrUs_outmz_r_outr-r-r.rs )$$  rc Kstt|||f\}}}||}t||}t|dkrtdd|vr(ttdd|vrOt|d}|dtd|d|d|d}t|||d}nd|vrYttdttd |||fS) a Find the optical setup conjugating the object/image waists. Parameters ========== wavelen : The wavelength of the beam. waist_in and waist_out : The waists to be conjugated. f : The focal distance of the element used in the conjugation. Returns ======= a tuple containing (s_in, s_out, f) s_in : The distance before the optical element. s_out : The distance after the optical element. f : The focal distance of the optical element. Examples ======== >>> from sympy.physics.optics import conjugate_gauss_beams >>> from sympy import symbols, factor >>> l, w_i, w_o, f = symbols('l w_i w_o f') >>> conjugate_gauss_beams(l, w_i, w_o, f=f)[0] f*(1 - sqrt(w_i**2/w_o**2 - pi**2*w_i**4/(f**2*l**2))) >>> factor(conjugate_gauss_beams(l, w_i, w_o, f=f)[1]) f*w_o**2*(w_i**2/w_o**2 - sqrt(w_i**2/w_o**2 - pi**2*w_i**4/(f**2*l**2)))/w_i**2 >>> conjugate_gauss_beams(l, w_i, w_o, f=f)[2] f rz,The function expects only one named argumentdistzD Currently only focal length is supported as a parameterrUr rrhzG The functions expects the focal length as a named argument) rLrr r#r&NotImplementedErrorrrr) r4waist_in waist_outkwargsrkrYrUrhrjr-r-r.rKs+    (   rNr/)'rB__all__sympy.core.exprrsympy.core.numbersrrsympy.core.sympifyr$sympy.functions.elementary.complexesrr(sympy.functions.elementary.miscellaneousr(sympy.functions.elementary.trigonometricrsympy.matrices.denserrsympy.polys.rationaltoolsrsympy.utilities.miscrrrrrrrrrr r r r r rrrr-r-r-r.s:      !##[ R 0