a must read
很幸運在ebay買到狀況跟新的差不多的二手書。
這本書內容相當豐富扎實，大致可分成三個部份，一到五章為第一部份，關於數位感光與訊號、成像、天文攝影等相關的基礎知識，詳細的說明了眼睛（感光細胞相當於多少micron的photosite，眼睛相當於多長焦距，眼睛量子效率多少等 ）與感光元件的photosite感光元的作用方式、規格，以及訊號與雜訊的產生，雜訊的泊松分佈方式與成份。
一切從E＝h c/λ這個公式開始 (h＝普朗克常數) 。這部份介紹了許多重要的基本知識，譬如天光（光害）與天體訊號的關係，與其雜訊的影響的（譬如天光再強也並不會淹沒天體訊號，只有它的雜訊才是關鍵），譬如像元與成像相關的運算，如何根據感光元規格以取樣或者FOV 的需求去選擇適合的焦長，在器材極限或seeing 極限時分別如何應對。又譬如影像校正的雜訊、訊噪比的變化，每經過一個處理程序都會伴隨其產生的雜訊。概括說是在counting the photons（書中這比喻很貼切，實際上每秒落在photosite的光子數的確也是手指可以數出來的）。
重點備忘（對照書閱讀）：
第一個暗的繞射環的直徑，在此圓內佔了84%能量linear diameter*＝d(Airy)=2.44 λ NN 焦比= Focal length/Aperture
如果是指角直徑則是 2.44 λ/A (A是物徑直徑)。
Rayleigh limit ＝Airy disk的半徑＝1.22 λ/A
FWHM of the diffraction disk＝1.02 λ N此圓內將近佔了一半的能量
而一個星點影像的FWHM是很基本且很重要的資訊，天文攝影（取樣、自動對焦等等）與影像處理有許多地方都需要計算到FWHM。FWHM可代表一個影像中能測量到的最小細節。
Dawes' Limit 約等於繞射極限的角分解能 λ/A (λ以550nm代入，為113.4/A), 主要應用在雙星解析，DL＝116/A （角秒）
眼球約等效16mm焦長焦比約F2.3~F11中央的錐狀細胞解析力達到眼球的解析度80角秒（人眼解析力據不同來源：40~120角秒）。感知顏色的錐狀細胞有三種，分別可感知藍綠紅三個範圍的波長，彩色數位相機的bayer陣列即模仿眼睛的顏色組成方式。
錐狀細胞並無法感應到連續波長，通常我們稱可見光波段（VIS）為400 至700nm，錐狀細胞為分別僅能感知紅、綠、藍三個波段的細胞。我們所見的“真實”世界的色彩如同透過濾鏡再組合成的。
視網膜攤平約40mm直徑，共一億個感光細胞。錐狀細胞大小約2 micro，視覺細胞的有效積分時間約100至200 milliseconds。量子效率極大值約 15% 在 505 nm。
*Behavioral measurements based on the FoS curve place the QE of the human eye between 0.03 and 0.06 (Retinal and post-retinal contributions to the quantum efficiency of the human eye revealed by electrical neuroimaging Gibran Manasseh, Chloe de Balthasar, [...], and Sara L. Gonzalez Andino )
看到人的視覺器官的量化資訊很有趣，自己將其與固態感光元件的規格相較令人更深刻。
Angular field of view of 感光元件視角大小＝2 arctan (焦距x 感光元件長/2) (弧角)。像元的解析角則以像元尺寸代入。Nyquist theorem取樣理論(critically sampled)一個畫素大小等於一半的繞射直徑（FWHM），而一顆星的繞射極限橫跨兩個畫素以上(3～5)叫oversampled。但受到seeing影響通常星點的大小不能達到繞射極限，這時取樣就對應PSF。從已知的像元大小求所需的焦長來達到所需FOV或取樣。取樣對應PSF當d (PSF) 大於等於 d(FWHM)Fl (min)=Aperture x d (pixel)/ （0.51＊ λ）常態分佈標準差99.7 %落在u±3 σ95.4％ u±2 σ68.3% u±σ
##光子訊號SNR=u /√u=√uu=平均值, √u=標準差光子雜訊是 poisson 分佈疊N張的SNR是√ （N *u)每個影像校正處理程序都會產生自己的雜訊，但會降低整體的雜訊S（raw)=x/g+x（dark)/g+bnoise : σ=1/g *√[σ(光子)^2＋暗σ(暗電流)^2＋σ(讀出雜訊)^2]在Dark sky下， 暗電流或讀出雜訊主宰 (detector or photon limited )
rural dark sky 天光的pixel值每分鐘約貢獻40顆光子差不多產生2.5個ADU雜訊x(total)=x (object) + x (sky) （電子）OSR= x (object) / x (sky)S (object) （pixel value）OSR=[S (object)- S (sky)]/ S(sky)亮目標 OSR可達1000, 暗淡目標則可小至0.001good suburban sky 一分鐘約600顆電子Urban Sky 一分鐘約4000顆電子
這部份也有簡單介紹望遠鏡器材的部份，但主要在說明要得到一個好成像品質的拍攝需注意的地方，如可能會遇上的一些影響影像品質的設備瑕疵、問題與解決方式，譬如彗差的簡單計算、Hot spots的可能來源，從瑕疵譬如塵點造成的平場影像中artifact的大小反推塵點在光路中可能位置，追蹤誤差的成份，包括週期誤差的原因，改善追蹤穩定度的小訣竅（非對稱平衡），也就是燈，對赤經軸來說，讓力矩稍微施向恆星時的另一方向，讓傳動元件吃點力，這對唸機械的我很合理，因為赤經軸的追蹤與導星都只會有一個方向，不是前進就是停止，所以受點力可以讓傳動件保持確實接觸。
第二部份從第六章到第十一章，包括影像校正程序的說明（Bias, light, dark, flat, flat dark 等校正），影像基本分析，感光元件性能簡單計算、測試，包括電子／ADU轉換率(g)，讀出雜訊、bias、熱訊號計算，線性度測試等。 然後是
天文測量學譬如影像中天體座標位置的計算，plate 座標與標準座的關係等。以及測光學，包括測光系統、濾鏡的發展，影像求raw instrumental magnitude，求消光係數及air mass的修正、色指數修正（二階消光係數），以及從器材星等轉換成標準星等，基本的測光規劃操作等。
第十一章是光譜學，簡單介紹光譜攝影的方式，稜鏡、Grism、光柵、光纖光譜儀的簡單結構介紹（簡單易懂的光路圖），散色元件的angular dispersion與成像 Dispersion (nm每pixel)與Resolving power計算，天體光譜的profile 提取等。
相機的效率是常被忽視的一環
重點備忘（對照書閱讀）：
暗電流校正的σ (combined)=√[σ(raw)^2/N(raw) + σ (dark) ^2/N(dark)]suburban sky 6 light 拍1 dark但dark sky noise limited建議1 light 拍3 darkN (dark)= [σ (dark)＾2/ σ (light) ＾2)]/N (light)S (flat)=S (raw) - S (dark)SNR (result) =1/√[1/SNR (image) ＾2 ＋ 1/SNR(flat)＾2]##感光元件的FOV約等於57.3 x dimension ccd /F (度)欲得相同大小FOV ,感光元件約大須越長焦多數梅西爾 15 min大小（視野選擇應比這大）Jupiter 40角秒組合視野建議80角秒 ，所以像素不需很多
Focal ratio matching
Planetary 當橡元大小10micron ,建議f/257 micron為 f/18550nm 的diffraction disk在 f/6 ＝ 3.4 micro
牛頓鏡彗差計算d(Coma ) =( 3/16)* h/ F^2h（mm）離軸高F焦距d(coma) f/4約是f/8的4倍修正後約等於未修正的f/8achromatic refractord(chromatic) = D/1700 mm##要注意field flooding, hot spots灰塵影像大小 P=D/dfP甜甜圈寬，d 畫素寬 D灰塵到感光元件距離方法評估曝光時間 e=[P (desired)/P(max) ]*(N^2/SB) 秒P(desired)目標值B＝ surface brightness, S＝ ISOＢ：M42 core 約0.001Rosette 約 5x10^-6 書中有各種天體值表格可参考
書中有自製平場燈箱的DIY方法如何拍攝一幅好影像的條件60秒增加到240秒增加1.5星等1min track and stack 累積也可達21等‘star testing astronomical telescopes’byH.R. suites星等乃比較的m1=-2.5log(F1/F2)+m2F1/F2=C1/C2c instrumental responses孔徑測光高斯 σFWHM =2.37 Gaussian σUBVRI 系統CI=mpg－mpv＋Cpg photographic 星等(藍版)pv photovisual 星等（黃板）CI=0 for A0 starsphotoelectric,tric color system(B-V)=0.16+0.92CIJohnson and MorganU,B,V(Visual)V0=Vx-k’(v) X-k"(v)X(b-v)xVx ran instrumental magnitude at V filterV0校正消光後的於大氣之上的instrumental magnitudeair mass X =sec ak’消光係數 （海平面0.24, 高海拔乾燥9.15)a天頂距二次消光可省略SR=FR*AR*TR*QR+SR skyAR 大氣透射率TR 濾鏡透射率QR光學系統與感光元件組合透射率FR flux紅色波段
第三部份就是數位影像處理在天文影像上的操作。這部份從第十二章到二十一章為止佔了本書一半的篇幅，裡面有不少數學運算程序（程式邏輯），不過如果有讀過數位影像處理那本聖經，就會發現其實都是熟悉的東西，但更深入、聚焦在與天文影像相關的，應該能很快進入狀況，幾種transfer function（即我們熟悉的曲線）包括特殊的鋸齒狀，另外，卷積（第十四章線性運算）的運算子的種類也介紹了好幾種天文影像處理相關的包括用來萃取特徵的 。
第十六章非線性運算子介紹了包括形態學與地形學相關的、很適合用在星系上的運算子，及偵測特徵的Frei and Chen 運算子，AIP4WIN 裡有提供這些運算。第十七章傅立葉理論是談影像在頻域裡的處理與轉換，傅立葉轉換與反轉換、其與卷積的重要關係，以及在頻域濾波的方式，包括mask, Butterworth filters的公式。還有能量不變的Larseval理論。
最後幾章也都是很重要且經典的影像處理，Fourier transform, Wavelet, deconvolution, 以及色彩相關處理包括G2V星或場星校正。wavelet noise filter 一節詳細說明了雜訊、標準差、特徵等關係，雜訊於wavelet每一階的變化，以及一個影像含泊松雜訊與高斯雜訊混合的雜訊可以轉換成一個純高斯雜訊的影像（Anscombe transform）以利進一步運算，以及其除噪的原理、方式運作；除此方式外，也介紹了更易運用的K-sigma小波濾鏡。
對兩函數的卷積做FFT=先對兩函數個別做FFT再相乘。Wavelet 的銳化即在小波分解後在需要的coefficient 上乘上一加權再全部加總回來。
deconvolution的過程是一個遞回評估到剩餘的雜訊(correction term = s(x,y)-k ⊗O(x,y))等於零, Van Cittert 加了一個relaxation parameter確保遞回收斂。Richardson-Lucy 的修正項是乘項，收斂為一。*在反卷積一個undersampled的影像前先將其resample 至少兩倍於期待影像的最高頻。
注意RGB濾鏡若有ir leak，必需加L(UV-ir blocking filter)
G2V星校正即拍攝一G2V星後計算其權重值。W(R)=S'(R G2V )/S(max), S'(R G2V)=T(R) Q(R), T 濾鏡的穿透係數，Q設備的穿透係數
以HSL color space調整的優點之一是L容易置換與處理而不會影響到顏色
從RGB製造一個訊噪比比各別濾鏡影像高的人工的L層：L=0.333 S'R+0.334 S'G+0.333 S'B
隨著感光元件等數位攝影的發展，對紅光的感光能力越來越強，曝光時間越來越長的趨勢，Ir leak的影響與應對方式不可忽視。
本書雖然是2005年的書，不過裡面的觀念都是很基礎的不變的東西，只有包含full-well参數的一張幾家感光元件的那張規格表因沒有更新可能算是有點過時了，以及那時CMOS的發展才剛要起飛對於CCD的評價仍高於CCD，雖說如此，那時也已經有背照式的sensor且量子效率已是90%了，只是還沒有普及，所以這本書讀到現在並不會覺得過時。
本書作者即是AIP4WIN天文軟體的作者，但它不是軟體手冊，但是書中會有些Tips告訴你如何利用此軟體提供的功能來處理書中提到的程序。附錄則有軟體操作指南。
應是疏誤：
*****
[轉載] Richard Berry
AIzp4WIN Groups.io
Hi all--
I have heard nothing from the AAS or S&T regarding sales of The Handbook of Astronomical Image Processing. According to Perry Remaklus of Willmann-Bell, the books were being moved from a warehouse to wherever the AAS wanted to store them, and that's the last I heard. I am grateful that the AAS decided to acquire Willmann-Bell's operations, and trust that they will in due time offer all the books that WB published.
The current version (second edition, fifth printing) is a solid-feeling softcover book that's 39 mm thick by 228 x 152 mm. The print job quality looks good. However, if you can locate a hardcover printing of the second edition, it will be essentially the same of the current version. Although we corrected small numbers of errors at each printing, there were no major changes from one printing to the next.
Regarding the rapidly changing CMOS camera technology, my advice is simple: for variable stars use the lowest gain setting because that will give you the greatest dynamic range. The readout noise level in CMOS cameras is typically 3 e- r.m.s., which is so low that you will nearly always be shot-noise limited. If you are worried about linearity, a realistic and easy check is to take a test series of images on a standard field using exposures in a half-magnitude step sequence, i.e., 1.0, 1.583, 2.512, 3.981, 6.309, 10.000, and then do photometry on the stars. Instrumental mags of stars should increase in half-magnitude steps if you get the mags directly from the ADU count, or remain constant if you compute the instrumental mags from the counts-per-second. It may take a few iterations to find the right times and test field, and it would be good if you do this to report your methods and results to this Group.
Before the Beachie Creek fire wiped out all but one of my telescopes, I experimented using my the Atik Horizon camera on my RASA 11 to make time series with a 10-second cadence. The resulting images had low dynamic range, of course, but yielded useable images in short exposure times. The problem I ran into were that my regular comp stars would be saturated. Unless you have some extraordinary need to raise the gain, stick to the lowest gain and the images will be very much like those from a CCD. In some respects, because CMOS cameras give you more controls to twiddle, people find it hard to resist the temptation to twiddle them. In a science camera, you want reliable unchanging performance. Period.
--Richard
AIzp4WIN Groups.io
Hi all--
I have heard nothing from the AAS or S&T regarding sales of The Handbook of Astronomical Image Processing. According to Perry Remaklus of Willmann-Bell, the books were being moved from a warehouse to wherever the AAS wanted to store them, and that's the last I heard. I am grateful that the AAS decided to acquire Willmann-Bell's operations, and trust that they will in due time offer all the books that WB published.
The current version (second edition, fifth printing) is a solid-feeling softcover book that's 39 mm thick by 228 x 152 mm. The print job quality looks good. However, if you can locate a hardcover printing of the second edition, it will be essentially the same of the current version. Although we corrected small numbers of errors at each printing, there were no major changes from one printing to the next.
Regarding the rapidly changing CMOS camera technology, my advice is simple: for variable stars use the lowest gain setting because that will give you the greatest dynamic range. The readout noise level in CMOS cameras is typically 3 e- r.m.s., which is so low that you will nearly always be shot-noise limited. If you are worried about linearity, a realistic and easy check is to take a test series of images on a standard field using exposures in a half-magnitude step sequence, i.e., 1.0, 1.583, 2.512, 3.981, 6.309, 10.000, and then do photometry on the stars. Instrumental mags of stars should increase in half-magnitude steps if you get the mags directly from the ADU count, or remain constant if you compute the instrumental mags from the counts-per-second. It may take a few iterations to find the right times and test field, and it would be good if you do this to report your methods and results to this Group.
Before the Beachie Creek fire wiped out all but one of my telescopes, I experimented using my the Atik Horizon camera on my RASA 11 to make time series with a 10-second cadence. The resulting images had low dynamic range, of course, but yielded useable images in short exposure times. The problem I ran into were that my regular comp stars would be saturated. Unless you have some extraordinary need to raise the gain, stick to the lowest gain and the images will be very much like those from a CCD. In some respects, because CMOS cameras give you more controls to twiddle, people find it hard to resist the temptation to twiddle them. In a science camera, you want reliable unchanging performance. Period.
--Richard
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