南開大學光學工程課件Sep-16th

1、Why are focusing instruments necessary?,Imaging In order to image S at location P, the time it takes for each and every portion of a wavefront leaving S to converge at point P must be identical. So:,Refraction at curved surface,where S0 and Si are the object and image distance measured from the vert

2、ex or pole V respectively. Obviously, this is the equation of a Cartesian Oval. S will be perfect imaged at P with the help of Cartesian Oval.,Refraction at curved surface,Imaging by a Flat refracting surface,The image formed by a flat refracting surface is on the same side of the surface as the obj

3、ect The image is virtual The image forms between the object and the surface The rays bend away from the normal since n1 n2,L,s,s,Refraction at a spherical surface Image we have a point source S (in other words, we have a point object S) whose spherical waves arrive at a spherical boundary of two tra

4、nsparent media. We prefer that the wave traveling in the second medium converges to a point S. In fact, it is also the basic requirement of optical instruments.,Refraction at curved surface,Refraction at curved surface,The upper figure depicts a wave from the point source S impinging on a spherical

5、interface of radius R centered at C. Here we assume n2n1.,Fermats Principle maintains that the optical path length (OPLSS) will be stationary （實際上，物與像之間根據(jù)費馬原理具有等光程性）, i.e.:,Refraction at curved surface,So we have:,Refraction at curved surface,which followed with,Discussion Sign convention for spheri

6、cal refraction surfaces and thin lenses,Refraction at curved surface,First order, paraxial or Gaussian optics With the paraxial condition (small values of ), we have sin= and cos=1. In this case, we have an approximation:,Refraction at curved surface,(1),P is called optical power. We could have this

7、 formula with Snells law rather than Fermats Principle.,Refraction at curved surface,The emerging wavefront segment corresponding to paraxial rays from a point source S is essentially spherical and will form a “perfect” image at its center point located at S.,Focus and focal length If an point is lo

8、cated at F0, where,Refraction at curved surface,according to equation (1), it is imaged at infinity (Si=). The location F0 is called first or object focus. And the special object distance is defined as the first or object focal length.,Refraction at curved surface,Similar, the second or image focus

9、is the axial point Fi where the image is formed when S0= . And the second or image focal length fi as equal to Si in the special case, we have,Refraction at curved surface,Refraction at aspherical surfaces Refraction at spherical surfaces is limited by paraxial condition. Refraction at aspherical su

10、rfaces will help us to perform many types of really “perfect” reshaping operation of light.,Refraction at curved surface,Perfect reshaping between converging (diverging) wave and flat wave With the help of ellipsoidal or hyper-boloidal surface, we can reshape precisely converging (diverging) waves i

11、nto plane wave or vice versa,Refraction at curved surface,Lens,第一章第6節(jié),LensWhat is a lens,What is a lens In traditional sense, a lens is an optical system consisting of two or more refractive interfaces where at least one of these is curved.,Type of lenses We limit ourselves centered systems of spher

12、ical surfaces (for which all the non-planar surfaces are centered on a common axis, or in other words, all surfaces are rotationally symmetric about a common axis),LensType of lenses,1. Simple lens and compound lens: Simple lens consist of one element, i.e., it only has two refracting surfaces Compo

13、und lens more than one elements. 2. Thin and thick lens: if its thickness is effectively negligible or not,LensType of lenses,3. Convex (converging or positive) lens and concave (diverging or negative) lens: With the assumption that the refractive index of the lens is larger than that of the environ

14、ment of the lens, convex lens is thicker at the center and so tends to decrease the radius of wavefronts. On the other hand, concave lens is thinner at the center and tends to cause the wavefronts to be more diverging than it was upon entry.,LensType of lenses,The simplest case thin-lens equations L

15、ets now locate the conjugate points for a lens of index nl surrounded by a medium of index nm. It is the simplest case of a lens.,LensThin-lens equations,From equation (1) we know that paraxial rays from S meet at P, a distance from V1 (Si1) given by:,Concerned the second surface, we find P serves a

16、s an object point of the second surface, a distance So2 away. Here:,The object space for the second interface containing P has an index nl, not nm, though it locations out of the lens. Since So2 is on the left and therefore positive while Si1 in the left and therefore negative, the formula is equal

17、to:,LensThin-lens equations,Equation (1) applied at the second surface yields:,(2),Here nlnm and R20, so that right-hand signal is positive. Combining equation (1) and (2) results in:,LensThin-lens equations,If the lens is thin enough (d0) and with a further simplification that the lens is in air (i

18、.e. nm 1),where we write So1=So and Si2=Si. It is often referred to as thin-lens equation or lens makers formula.,LensThin-lens equations,If the indices of the media at left and right parts of the lens is different, let say n1 and n2, the formula for conjugate point S and P is,LensThin-lens equation

19、s,Focal length,Gaussian lens formula Let go back to the case that lens is in air. For a thin lens, fi=fo=f. we have:,It is the famous Gaussian lens formula.,LensThin-lens equations,Focal points,LensThin-lens equations,Focal plane Let think about bundles of parallel paraxial rays when several bundles

20、 enter in a narrow cone. They will be focused on a spherical segment centered on C.,Since the ray cone must indeed be narrow, can satisfactorily be represented as a plane normal to the symmetry axis and passing through the image focus. It is known as a focal plane.,LensThin-lens equations,Finite ima

21、gery We have dealt with the image of a single-point source. Now lets go further to the case that a great many such points combining to form a continuous finite object. Within the restrictions of paraxial theory, a small planar object normal to the optical axis will be imaged into a small region also

22、 normal to that axis.,LensThin-lens equations,1. Position on the optical axis With the similar discussion as for the case of the point source, we have,It is the Newtonion form of the lens equation which first appeared in “Opticks” written by Newton at 1704,LensThin-lens equations,2. Transverse or lateral magnification It is quit interesting and practically important to make clear the ratio of the transverse dimensions of the final image formed by any optical system to the corresponding dimension of the object which is referred as lateral or transverse m