本論文提出影印機三個焦段之變焦鏡頭鏡設計，目的設計出一個可分別
影印紙張A3、B4 及A4 之尺寸。選定鏡頭第一焦段到第三焦段F/#依次為
F/4.2183、F/4.4936、F/4.7692，光源的波長是以F-line、d-line、C-line 為設計，參考波長為d-line。
本系統物像距離固定，即紙張與感測器的距離保持固定。已知A3、B4、
A4 紙張寬度分別為297 mm、250 mm、210 mm。選用Toshiba CCD 線性感測器，有效長度為35.015 mm，可分別求出第一焦段放大率m1= -0.11789、第二焦段放大率m2= -0.14005、第三焦段放大率m3= -0.16673。已知感測器像素尺寸為4.7 m，則可判讀紙張A3、B4、A4 解析度分別為637 dpi、756dpi、901 dpi。
本變焦鏡頭設計有八片鏡片，其中三片玻璃球面鏡片，五片塑膠非球面
鏡片。其光學品質分別為: 第一焦段之MTF(80 lp/mm) 58.4%，|TMTFSMTF| 5.3%，光學畸變 1.95%，橫向色差絕對值 1.796 μm，相對照度
89.13%。第二焦段之MTF(80 lp/mm) 57.5%，|TMTF-SMTF| 5.5%，光學
畸變絕對值 1.65 %，橫向色差 1.020 μm，相對照度 91.72%。第三焦段
之MTF(80 lp/mm) 57.9%，|TMTF-SMTF| 3.8%，光學畸變絕對值 1.17%，

A 3× zoom lens design for a copy machine is presented. The purpose of the
design is to make copies respectively with the paper size A3、B4 and A4. Selecting
the F/# of Zoom1 to Zoom3 are F/4.2183、F/4.4936、F/4.7692 . Using the
spectrum F-line, d-line, C-line, and d-line is for the reference wavelength.
The total track of this 3× zoom system is fixed, which means the distance of
paper to the sensor is fixed. Given the paper width A3, B4, A4 which are 297 mm,
250 mm, 210 mm. Selecting Toshiba linear CCD for the image sensor and the
effective length is 35.015 mm. Obtaining the result of magnifications about
Zoom1 to Zoom3 are m1= -0.11789, m2= -0.14005 ,m3= -0.16673. Given the size
of the image sensor is 4.7 m, then the resolution of A3, B4, A4 are 637 dpi, 756
dpi, 901 dpi.
The 3× zoom lens design consists of three spherical and five aspherical
lenses. For the Zoom1’s quality of imaging , the value of the MTF 58.4 % at 80
lp/mm with a value of |TMTF-SMTF|  5.3 %. The optical distortion  1.95 %
and the lateral chromatic aberration  1.769 μm. The relative illumination 
89.13 %. For the Zoom2’s quality of imaging , the value of the MTF  57.5 % at
80 lp/mm with a value of |TMTF-SMTF|  3.8 %. The optical distortion  1.65 %
and the lateral chromatic aberration  1.020μm. The relative illumination 
91.72%. For the Zoom3’s quality of imaging , the value of the MTF  57.9 % at
80 lp/mm with a value of |TMTF-SMTF|  6.5 %. The optical distortion  1.17%
and the lateral chromatic aberration  1.330μm. The relative illumination  89.69
%.

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