changed the prototype stuff from the bottom into a new angular-psf function

[woropt.git] / lens.lisp

(defpackage :lens
  (:use :cl)
  (:export #:norm
           #:plane-ray
           #:lens-ray
           #:thin-objective-ray
           #:back-focal-plane-radius
           #:focal-length-from-magnification
           #:etendue
           #:oil-objective-etendue
           #:magnification-from-angles
           #:mirror-ray
           #:m
           #:v
           #:rotation-matrix
           #:m*
           #:cross
           #:make-thin-objective
           #:rotate-vector
           #:find-inverse-ray-angle))

;; for i in `cat lens.lisp|grep "^(defun"|cut -d " " -f2`;do echo \#:$i ;done
(in-package :lens)

(declaim (optimize (speed 2) (safety 3) (debug 3)))

(deftype vec ()
  `(simple-array double-float (3)))

(deftype mat ()
  `(simple-array double-float (3 3)))

(declaim (ftype (function (&optional double-float double-float
                                     double-float)
                          (values vec &optional))
                v))
(defun v (&optional (x 0d0) (y 0d0) (z 0d0))
  "Create a vector."
  (make-array 3 :element-type 'double-float
              :initial-contents (list x y z)))

(declaim (ftype (function (vec vec)
                          (values double-float &optional))
                v.))
(defun v. (a b)
  "Dot product between two vectors."
  (let ((sum 0d0))
    (declare (double-float sum))
    (dotimes (i 3)
      (incf sum (* (aref a i)
                   (aref b i))))
    sum))

(declaim (ftype (function (vec vec)
                          (values vec &optional))
                v- v+))
(defmacro v-op (op a b)
  "Subtracting and adding vectors."
  `(let ((result (v)))
     (dotimes (i 3)
       (setf (aref result i) (,op (aref ,a i)
                                  (aref ,b i))))
     result))

(defun v+ (a b)
  "Add two vectors."
  (v-op + a b))

(defun v- (a b)
  "Subtract two vectors."
  (v-op - a b))

(declaim (ftype (function (vec double-float)
                          (values vec &optional))
                v*))
(defmethod v* (a scalar)
  "Multiply vector with scalar."
  (declare (double-float scalar)
           (vec a))
  (let* ((result (v)))
    (dotimes (i 3)
      (setf (aref result i) (* scalar (aref a i))))
    result))

(declaim (ftype (function (vec)
                          (values double-float &optional))
                norm))
(defun norm (a)
  "Length of a vector."
  (let ((l2 (v. a a)))
    (declare (type (double-float 0d0) l2)) ;; Otherwise warning with complex-double
    (sqrt l2)))

(declaim (ftype (function (vec)
                          (values vec &optional))
                normalize))
(defmethod normalize (a)
  "Rescale vector to unit length."
  (v* a (/ (norm a))))

(declaim (ftype (function (disk vec vec)
                          (values vec (or null vec) &optional))
                plane-ray))
(defun plane-ray (disk ray-start ray-direction)
  "Find the point where a ray intersects a plane. It returns two
vectors first the unchanged direction of the beam and then the
intersection point. The ray is defined by one position RAY-START and a
direction RAY-DIRECTION. The plane is defined by a point PLANE-CENTER
and its normal PLANE-NORMAL."
  (with-slots (center normal)
      disk
    (let* ((hess-dist (v. center normal)) ;; distance of plane to origin
           (div (v. normal ray-direction)))
      (if (< (abs div) 1d-13)
          ;; plane and ray are parallel and don't intersect
          (values ray-direction nil)
          (let ((eta (/ (- hess-dist (v. normal ray-start))
                      ;; scaling along ray to hit exactly on plane
                      div))) 
            (values ray-direction
                    (v+ ray-start (v* ray-direction eta))))))))
#+nil
(plane-ray (make-disk) (v 0d0 .1d0 -1d0) (v 0d0 0d0 1d0))

;;
;;                 --\
;;                |   -----\   intersection
;;                |         --+
;;         |       \       ---|--\
;;         |       | -----/   |   ----\
;;         |   ----+/   r'    |        ----\
;;       f |--/    c          |             ----\      dir
;;         |    r             |                  ---\
;;         |                  |rho                   ----\
;;         |                  |                           ----\
;;         |                  |                                ----\
;;         |                  |                           phi       ----\
;;  -------+----------<-------+-------------------------------------------
;;         |             n    | center
;;         |                  |
;;         |                  |
;;         |                  |
;;                            |
;;                    f       |


(declaim (ftype (function (lens vec vec
                                &key (:normalize boolean))
                          (values (or null vec) vec &optional))
                lens-ray))
(defun lens-ray (lens
                 ray-start ray-direction
                 &key (normalize t))
  "Return new ray-direction and intersection after thin lens."
  (with-slots (center normal focal-length radius)
      lens
    (unless (< (abs (- 1 (norm ray-direction))) 1d-12)
      (error "ray-direction doesn't have unit length"))
   (unless (< (abs (- 1 (norm normal))) 1e-12)
     (error "lens-normal doesn't have unit length"))
   (multiple-value-bind (dir intersection)
       (plane-ray lens
                  ray-start ray-direction)
     (declare (ignore dir))
     (let* ((rho (v- intersection center)))
       (format t "~a~%" (list 'intersection intersection 'center center
                              'rho rho 'norm (norm rho)))
       (unless (< (norm rho) radius)
         (return-from lens-ray (values nil intersection)))
       (let* ((cosphi (v. normal ray-direction))
              (r (v- (v* ray-direction (/ focal-length cosphi))
                     rho)))
         (values (if normalize
                     (normalize r)
                     r) intersection))))))
#+nil
(lens-ray (make-lens)
          (v 0d0 .1d0 -2d0)
          (v 0d0 0d0 1d0))

;;
;;                                 |
;;                                 |
;;  ---------------     s          |
;;-/               X----           |
;;                /     \-- ----   |
;;             ro/         \--  \--+----
;;               |          ----/  |    \-------
;;              /     -----/    \  |            \------
;;             / ----/ ru        \ |                   \-------
;;            /-/                 \|rho                        \-------
;;                                 |                                   \---
;;                                 |
;;   ------------------------------+-----------------------------------------
;;                                 |
;;             |        nf         /
;;             +--------------------
;;             |                 /

(declaim (ftype (function (thin-objective
                            vec vec)
                          (values (or null vec) vec &optional))
                thin-objective-ray))
;; 2008 Hwang Simulation of an oil immersion objective lens...
(defun thin-objective-ray (objective
                           ray-start ray-direction)
  "Returns direction of outgoing ray and intersection with principal
sphere. If this sphere isn't hit inside the maximum angle (given by
NA), then nil as a direction and the intersection with the
lens-surface is returned instead."
  (with-slots (center normal focal-length
                      radius ;; bfp-radius
                      immersion-index numerical-aperture)
      objective
    (unless (< (abs (- 1 (norm normal))) 1d-12)
      (error "lens normal doesn't have unit length"))
   (unless (< (abs (- 1 (norm ray-direction))) 1d-12)
     (error "ray-direction doesn't have unit length"))

   (multiple-value-bind (r intersection)
       (lens-ray objective
                 ray-start ray-direction :normalize nil)
     (unless r
       (return-from thin-objective-ray (values nil intersection)))
     (let* ((a (v* normal (* focal-length (- immersion-index 1))))
            (ru (v+ r a))
            (rho (v- intersection center))
            (rho2 (v. rho rho))
            (nf (* immersion-index focal-length))
            (nf2 (* nf nf))
            (rat (- nf2 rho2)))
       (unless (<= 0d0 rat)
         (return-from thin-objective-ray (values nil intersection))
         #+nil  (error "ray can't pass through objective"))
       (let* ((s (v* ray-direction (- nf (sqrt rat))))
              (ro (v- ru s))
              (cosu (v. ro normal))
              (sinu2 (- 1 (* cosu cosu)))
              (sinu-max (/ numerical-aperture immersion-index)))
         (unless (<= sinu2 (* sinu-max sinu-max))
           (return-from thin-objective-ray (values nil intersection)))
         (values ro (v+ s intersection)))))))

#+nil
(thin-objective-ray (v 0d0 0d0 0d0)
                    (v 0d0 0d0 -1d0)
                    2.3d0 1.515d0
                    (v 0d0 1d0 10d0)
                    (normalize (v 0d0 0d0 -1d0)))


;;                      |
;; --------             |
;;   SS    \---         |
;;             \--      |
;;                X-----+-------------------------------
;;              /-  \   |
;;            /-     \  |
;;    nf=h  /-        \ | D/2=R
;;        /-           \|
;;      /-              |
;;    /- alpha          |
;; ---------------------+----------------------------------------
;;             nf       |
;;
;; sin(alpha) = R/nf


(declaim (ftype (function (double-float double-float)
                          (values double-float &optional))
                back-focal-plane-radius))
(defun back-focal-plane-radius (focal-length numerical-aperture)
  (* focal-length numerical-aperture))
#+nil
(back-focal-plane-radius 2.61d0 1.4d0)

(declaim (ftype (function (double-float)
                          (values double-float &optional))
                focal-length-from-magnification))
(defun focal-length-from-magnification (mag)
  (/ 164.5 mag))
#+nil
(focal-length-from-magnification 63d0)

(declaim (ftype (function (double-float double-float
                                        &optional  double-float
                                        double-float double-float)
                          (values double-float &optional))
                etendue))
(defun etendue (chief-height marginal-angle
                &optional
                (refractive-index 1d0)
                (marginal-height 0d0) (chief-angle 0d0))
  (let ((q (- (* chief-height refractive-index marginal-angle)
              (* marginal-height refractive-index chief-angle))))
    (* q q)))
#+nil
(etendue .07d0 (* 67d0 (/ pi 180)) 1.515d0)


(declaim (ftype (function (double-float &optional double-float
                                        double-float)
                          (values double-float &optional))
                oil-objective-etendue))
(defun oil-objective-etendue (field-radius &optional (numerical-aperture 1.4d0)
                              (refractive-index 1.515d0))
  (let ((rat (/ numerical-aperture refractive-index)))
    (unless (<= (abs rat) 1)
      (error "impossible angle, check numerical aperture and refractive index."))
   (let* ((marginal-angle (asin rat)))
     (etendue field-radius marginal-angle refractive-index))))
#+nil
(oil-objective-etendue .07d0)

(declaim (ftype (function (double-float double-float
                                        &optional double-float double-float)
                          (values double-float &optional))
                 magnification-from-angles))
(defun magnification-from-angles (u uu &optional (n 1d0) (nn 1d0))
  "u is the objects marginal ray angle and uu for the image."
  (/ (* n (sin u))
     (* nn (sin uu))))

(declaim (ftype (function (mirror vec vec)
                          (values (or null vec) vec &optional))
                mirror-ray))
;;   sketch of the mirror for incoming parallel light
;;   --------------------+-----------------------
;;                    /|\
;;                   / | \
;;                  / n|  \            N=n*(- (p.n))
;;              q  /   |   \  p        p+N=r
;;                /    v    \          q=N+r
;;               /           \
;;              /      |      \        q=p-2(p.n)*n
;;             /       |       \
;;            /       N|        \
;;           /         |         \
;;          /          |     r    \
;;         /           v<----------\
;; p .. ray-direction
;; N .. mirror-normal

(defun mirror-ray (mirror ray-start ray-direction)
  "Mirror center C, mirror normal N.
Return reflected direction and intersection. If the ray isn't inside
of the radius return nil and the intersection."
  (with-slots (center normal radius)
      mirror
    (unless (< (abs (- 1 (norm normal))) 1d-12)
      (error "mirror normal doesn't have unit length"))
   (unless (< (abs (- 1 (norm ray-direction))) 1d-12)
     (error "ray-direction doesn't have unit length"))
   (multiple-value-bind (dir intersection)
       (plane-ray mirror ray-start ray-direction)
     (declare (ignore dir))
     (unless (< (norm (v- intersection center)) radius)
       (return-from mirror-ray (values nil intersection)))
     (let ((dir (v+ ray-direction (v* normal
                                      (* -2d0 (v. ray-direction normal))))))
       (values dir intersection)))))

(declaim (ftype (function (double-float double-float double-float
                                        double-float double-float double-float
                                        double-float double-float double-float)
                          (values mat &optional))
                m))
(defun m (a b c d e f g h i)
  (make-array '(3 3)
              :element-type 'double-float
              :initial-contents (list (list a b c) (list d e f) (list g h i))))

(declaim (ftype (function (double-float vec)
                          (values mat &optional))
                rotation-matrix))
(defun rotation-matrix (angle vect)
  "Create matrix that rotates by ANGLE radians around the direction
 VECT. VECT must be normalized."
  (let* ((u (aref vect 0))
         (v (aref vect 1))
         (w (aref vect 2))
         (c (cos angle))
         (s (sin angle))
         (1-c (- 1 c))
         (su (* s u))
         (sv (* s v))
         (sw (* s w)))
    (m (+ c (* 1-c u u))
       (+ (* 1-c u v) sw)
       (- (* 1-c u w) sv)

       (- (* 1-c u v) sw)
       (+ c (* 1-c v v))
       (+ (* 1-c v w) su)

       (+ (* 1-c u w) sv)
       (- (* 1-c v w) su)
       (+ c (* 1-c w w)))))
#+nil
(rotation-matrix (/ pi 2) (v 0d0 0d0 1d0))

(declaim (ftype (function (mat vec)
                          (values vec &optional))
                m*))
(defun m* (matrix vect)
  "Multiply MATRIX with VECT. Copies 4th component w from VECT into
result."
  (let ((res (v)))
    (dotimes (i 3)
      (dotimes (j 3)
        (incf (aref res i)
              (* (aref matrix i j) (aref vect j)))))
    res))
#+nil
(m* (rotation-matrix (/ pi 2) (v 0d0 0d0 1d0)) (v 1d0))

(declaim (ftype (function (vec vec)
                          (values vec &optional))
                cross))
(defun cross (a b)
  (v (- (* (aref a 1) (aref b 2))
        (* (aref a 2) (aref b 1)))
     (- (* (aref a 2) (aref b 0))
        (* (aref a 0) (aref b 2)))
     (- (* (aref a 0) (aref b 1))
        (* (aref a 1) (aref b 0)))))
#+nil
(cross (v 1d0)
       (v 0d0 1d0))

(deftype optical-component ()
  `(or disk mirror lens thin-objective))


(defstruct ray
  (start (v) :type vec)
  (direction (v) :type vec))

(defstruct disk
  (normal (v 0d0 0d0 1d0) :type vec)
  (center (v) :type vec)
  (radius 1d0 :type double-float))

(defstruct (mirror (:include disk)))

(defstruct (lens (:include disk))
  (focal-length 1d0 :type double-float))

(defstruct (thin-objective (:include lens))
  (immersion-index 1.515d0 :type double-float)
  (numerical-aperture 1.38d0 :type double-float))

(declaim (ftype (function (double-float vec vec)
                          (values vec &optional))
                rotate-vector))
(defun rotate-vector (angle axis vector)
  (let ((m (rotation-matrix angle axis)))
    (m* m vector)))

;;        +-------+--
;;        |       |  \-----
;;     h  |       |        \-----
;;        |       |              \----
;;        |       |        phi        \-----
;;   -----+-------+------------o------------\------------------------
;;         (n-1)f     f               f
(declaim (ftype (function (double-float double-float thin-objective)
                          (values double-float &optional))
                find-inverse-ray))
;; 2005wolf p. 180 formula (8) sine condition for one image in infinity 
(defun find-inverse-ray-angle (point-x point-y objective)
  "Find the angle in the back focal plane for a ray that originates
from a POINT in the object. The coordinates of the point are given
relative to the center of the front focal plane."
  (with-slots (focal-length)
      objective
    (let* ((h (sqrt (+ (* point-x point-x) (* point-y point-y))))
           (phi (asin (/ h focal-length))))
      phi)))

#+nil
(let* ((f (focal-length-from-magnification 63d0))
       (na 1.38d0)
       (ri 1.515d0)
       (bfp-radius (back-focal-plane-radius f na))
       (obj (make-thin-objective :normal (v 0d0 0d0 -1d0)
                                 :center (v 0d0 0d0 (- f))
                                 :focal-length f
                                 :numerical-aperture na
                                 :immersion-index ri))
       (field (v .0d0 0d0 (- (+ f (* ri f)))))
       (pupil (v bfp-radius 0d0 0d0)))
  (list bfp-radius f (find-inverse-ray-angle 0 .07 obj)))