| 摘要: | 鏡頭製造組裝公差是每一家鏡頭光學廠必需面對的問題，但其加工成本與光學成像品質，每家光學廠差異很大技術也不同。本文為玻璃鏡片材料特性探討與鏡片製造和鏡頭組裝公差對其鏡頭成像品質分析。
本論文首先分析玻璃鏡片之折射率與波長關係，玻璃化學性質與相對價格，設計時要考慮材料的價格，這樣可以設計出便宜且成像品質好的鏡頭，因為會使用非球面玻璃鏡片，所以要使用Tg值小於550C的玻璃材料。
因為設計時不能只考慮室溫環境，還要考慮溫度變化下所造成的影響，要分析玻璃折射率與溫度變化的關係。溫度變化與熱膨脹係數會對鏡片參數的影響，不同的鏡片材料有不同的熱膨脹係數，在溫度變化後鏡片的參數會改變，像是曲率半徑、鏡片厚度、空氣間隙以及非球面係數，還要考慮鏡片折光率與溫度關係，鏡片折光率可以利用鏡筒材料的熱膨脹係數或是不同鏡片材料的熱膨脹係數互相補償，最終達到消熱差的目的。
光學畸變在半視角θ近似90時，tan90=，則近軸像高為無限大，但真實像高不可能為無限大，如果鏡頭優化設計過程，光學畸變還是以理想像高為目標值，則真實像高在半視角75至90之間，真實像高無法急遽增大，所以真實像高會成一定值，其影像會重疊在一起。為改變此情形需改變理想像高之定義，使理想像高變成線性變化，故在設計大角度或廣角鏡頭設計時，為了避免此缺點採用F-theta畸變來判斷成像面扭曲程度。且人眼對於光的變化很敏感，人眼會察覺畫面中心亮度與邊緣有差異，所以設計時要考慮相對照度。
在製造與組裝時會產生公差，而公差會讓設計完成的光學系統的成像品質下降，公差容忍度越小的元件代表製造上越困難且價格越高，增加成本的壓力以及製造難度，因此在元件的公差設定上，要讓公差容忍範圍變大且不會犧牲太多鏡頭品質，這樣不僅能降低成本，在製造上也能更容易。最後在分析CODE V中的公差分析計算鏡頭製造良品率之累計機率函數分布， CODE V 所使用的機率就是2σ的機率分布，代表97.7%的機率製造出的系統會有這種性能。
最後再把這些理論實際應用在掃描器鏡頭設計，藍光光學讀寫頭光路設計，手機鏡頭設計，監視器廣角鏡頭設計，設計必須要達到自己的設計目標。
;Lens manufacturing assembly tolerance is a necessary issue for every lens optical factory, but its processing cost and optical imaging quality vary greatly from one optical factory to another with different technologies. This paper is analysis of glass lens material characteristics and lens manufacturing and lens assembly tolerances on its lens imaging quality.
This paper first analyzes the relationship between refractive index and wavelength of glass lenses, the chemical properties of glass and the relative price, and the price of the material should be considered when designing, so that a cheap lens with good imaging quality can be designed, because aspheric glass lenses will be used, so glass materials with a Tg value less than 550C should be used.
Because the design should not only consider the room temperature environment, but also consider the effect of temperature change, and analyze the relationship between the refractive index of glass and temperature changes. The temperature change and thermal expansion coefficient will affect the lens parameters. Different lens materials have different thermal expansion coefficients. After the temperature changes, the lens parameters will change, such as the radius of curvature, lens thickness, air gap and aspheric coefficient. The relationship between the optical power of the lens and the temperature, the refractive index of the lens can be compensated by the thermal expansion coefficient of the lens barrel material or the thermal expansion coefficient of different lens materials, and finally achieve the purpose of heat dissipation.
Optical distortion in the half-view angle θ approximation 90, tan90=, then the paraxial image height is infinite, but the real image height can not be infinite, if the lens optimization design process, optical distortion or the ideal image height as the target value, then the real image height in the half-view angle between 75 and 90, the real image height can not increase sharply, so the real image height will become a certain value, the image will overlap together. In order to change this situation, the definition of ideal image height needs to be changed, so that the ideal image height becomes a linear change, so in the design of large angle or wide-angle lens design, in order to avoid this shortcoming to use F-theta distortion to determine the degree of distortion of the imaging surface. And the human eye is sensitive to changes in light, the human eye will notice the difference between the brightness of the center of the picture and the edge, so the design should consider the relative illumination.
There will be tolerances during manufacturing and assembly, and tolerances will degrade the imaging quality of the designed optical system. Components with smaller tolerances mean more difficult manufacturing and higher prices, increasing cost pressure and manufacturing difficulty. Therefore, in the tolerance setting of the components, the tolerance range should be enlarged without sacrificing too much lens quality. This will not only reduce the cost, but also make it easier to manufacture. Finally, analyze the tolerance analysis in CODE V to calculate the cumulative probability function distribution of the lens manufacturing yield. The probability used by CODE V is the probability distribution of 2σ, which means that the system manufactured with a 97.7% probability will have this performance.
Finally, apply these theories to the design of the scanner lens, the optical path design of the Blu-ray optical read-write head, the design of the 2 million pixels mobile phone lens, and the design of the wide-angle lens of the monitor. The design must achieve its own design goals. |
