以上是傍軸近似的理論體系，我們可以看到從簡(jiǎn)單的透鏡開始，研究了近軸光學(xué)的特點(diǎn)。這部分內(nèi)容在幾何光學(xué)的書籍中均有涉及，只是有的書很清晰，有的書含糊其辭的講了一下，并沒有說清楚。近軸光學(xué)所應(yīng)用的條件和特點(diǎn)，可以說單個(gè)的透鏡是系統(tǒng)總和的支撐，所以這一部分理論是光學(xué)系統(tǒng)設(shè)計(jì)的基石。
英文翻譯要求不是要求一一對(duì)應(yīng)，而是要準(zhǔn)確的翻譯出所要表達(dá)的內(nèi)涵，在中文書中尋找對(duì)應(yīng)的關(guān)系和補(bǔ)充。
General Remarks
The property屬性 of an optical system in which all rays that are emitted發(fā)出 by an object at point O meet in an image at point O' is called optical imaging.
principle of image formation by a common ray intersection point.????????共射線交點(diǎn)成像原理
Real images which have a positive image distance from the vertex頂點(diǎn) and which can be made visible by a ground glass screen are distinguished區(qū)別 from virtual images with a negative focal distance.in the case of such a virtual image,the rays meet when they are extended backwards.which have a positive image distance from the vertex頂點(diǎn) and which can be made visible by a ground glass screen are distinguished區(qū)別 from virtual images with a negative focal distance.in the case of such a virtual image,the rays meet when they are extended backwards.
In order to calculate the location and size of the images in the paraxial approximation 近軸近似 classical lens formula or Newton's equation can be used.These are discussed in the following chapters.This field of paraxial optics is also called Gaussian optics.
paraxial Approximation
In geometric ?optics the law of refraction at dielectric interfaces or mirrors determines the ray path through the system. ? ? ?在幾何光學(xué)中，介質(zhì)界面或反射鏡的折射定律決定光線穿過系統(tǒng)的路徑。
It is written as????
where n and n' are the refractive indices before and behind the refraction of the ray,I and I' are the incidence angles in the two media.The paraxial approximation can be developed from the exact imaging equations by linear approximation of the sine function in the law of refraction.The Taylor series of the sine function
is truncated after the first term
and delivers the law of ?refraction in its paraxial form.Writing small characters i and i' for the paraxial approximated incidence angles in order to distinguish them,this can be written
傍軸近似在小角度下誤差屬于高階誤差，關(guān)系幾乎為線性的。
Image Locations
The simple optical system that can produce an image is a single lens or a mirror.Therefore the differences resulting from the formation of real or virtual image locations are disscussed using the
example of a single lens.
能產(chǎn)生圖像的最簡(jiǎn)單的光學(xué)系統(tǒng)是一個(gè)透鏡或一個(gè)鏡子。因此，用一個(gè)透鏡的例子來討論實(shí)際或虛擬圖像位置的形成所產(chǎn)生的差異。 ? ? ??
看似可有可無的一句話，確也是有理有據(jù)。
????????For different values of the object distance,the image formation produced by a single lens can seen in figure 2-3 to 2-7 ,see also 2-2 and 2-3 .An object positioned whithin the focal length of a convergent lens usually leads to a virtual image,while outside,real images are produced at finite distances.The magnification m is equal to 1 only for an object positioned at twice the distance from the focal point.For objects at a greater distance,the image will be reduced in size.
????????The main examples for the paths of rays passing through a positive lens,depending on the positon of the object,are shown in figure 2-3.
? ? ? ? For a single negative lens the image is principally virtual,as shown in figure 2-4.
? ? ? ? The focal points F and F' are particular points of a lens or an imaging system (see also the chapter concerning the cardinal points of a lens).A ray incident to a lens which is parallel to the optical axis intercepts the aixs at the focal point F' behind the lens.Coversely,a ray running through the front focal point F will be parallel to the axis behind the lens.
? ? ? ? For simplification we first consider a thin lens whose optical effect can be imagined as taking place of the lens.The distances from the focal points to the lens are called the focal lengths f and f',respectively.Furthermore, r is the object height measured perpendicular to the axis and r'?is the corresponding image height.The distances of object and image positions from the lens are labelled s and s'.
? ? ? ? The sign convention which is used in optic considers distance along the optical axis as positive if they are oriented in the sense of a vector in the positive z direction.The same applies for the r and x coordinates perpendicular to the axis.Then in the case of real imaging through a single positive lens with a positive object of height r?and image height r',the distance form the vertex s and the focal length f are negative,whereas the quantities s' and f' are positive.
? ? ? ? A positive lens with a focal length of f'>0 produces a real image as long as the distance of the object from the vertex is greater than the focal length.
一個(gè)焦距為F＞0的正透鏡，只要物體與頂點(diǎn)的距離大于焦距，就產(chǎn)生一個(gè)真實(shí)的圖像。
