Further statistical analysis of the visual observational sketch database of 300 deep-space objects at Anbu
(Part 2). Analysis of the observational data of the 300 objects, including analysis of visual threshold of extended objects such as galaxies and nebulae.
(updated 2023/07/11) 修正與新增圖表 new charts
以半光度半徑 half-light radius（即effective radius, 以下簡稱半光徑）評估
由於鞍部以小望遠鏡眼視星系與球狀星團所能見的大小極為接近半光徑的範圍，且因為它們的brightness profile 有集中於中心並向外圍遞減的特性，與其他如發射星雲等延伸天體平坦的亮度分佈差異很大。所以這裡星系與球狀星團另外以半光徑來製作圖表分析，以求更為貼近實際的狀況。
將資料庫中目前有Effective Radius/half-mass Radius 資料的約140個左右的天體 (星系、球狀星團)，及其他表面亮度分佈較平坦的有面積天體（星雲，沿用短直徑b），共219個樣本數製作圖表。其中可計算出對比門檻值的有164個樣本。
Evaluation using the half-light radius
Since the sizes of galaxies and globular clusters visible to the naked eye through small telescopes in Anbu are very close to the range of the half-light radius, the galaxies and globular clusters here are analyzed using the half-light radius for charting purposes.
Approximately 140 Deep sky objects (galaxies, globular clusters) with available data on the effective radius/half-mass radius, along with other extended objects with area data (using short diameter 'b'), were used to create a chart with a total of 219 samples. There are 164 samples with a calculable contrast threshold.
結論
將300 個眼視觀測素描其中屬於延伸天體（星系、星雲，此外，球狀星團也可視為延伸天體）的觀測數據作統計分析後，圖表與將Blackwell於 1946的人眼辨識對比門檻的實驗（'Contrast Thresholds of the Human Eye'）結果所應用在天文眼視觀測上的理論相當吻合。這個三百天體眼視素描資料庫/試算表應可普遍應用於眼視觀測中，會因人而異的因素不多。
After conducting statistical analysis on the observational data of 300 visual sketches, which belong to extended celestial objects such as galaxies, nebulae (in addition, globular clusters can also be considered as extended objects), the results obtained from the analysis align well with the theoretical application of Blackwell's 1946 experiment on contrast thresholds of the human eye in astronomical visual observations.This 300 object visual observations and sketches database/spreadsheet should be generally applicable to visual observations, with few individual variations due to personal factors.
資料庫參數說明
除了我的觀測資料外，我也補充了天體的一些相關數據，同時增加了測試天空亮度、倍率、濾鏡的功能，可以不同的觀測條件去測試可見度（當有測試值時試算表會以測試數據取代我的觀測數據去計算contrast），即Contrast threshold，在該條件下該目標的可偵測表面亮度，只要天體放大倍率後的亮度比這門檻亮，即表示可見（這個數據僅供參考）。
對比門檻理論主要來自 Blackwell 1946年的人眼對比門檻實驗，我參考了 Roger N. Clark的“Visual Astronomy of the Deep Sky”（它可能是第一本系統性的將Blackwell的實驗結果運用到眼視觀測上的書籍），另外我也學習了加拿大皇家天文學會的 contrast threshold試算表的估算方式。
試算表中“Out of size range"表示放大後的尺寸已超過Blackwell實驗的最大尺寸360'，因此無法計算。而資料庫與統計圖表中的contrast threshold 的正負0.7 mpsas 誤差誤差主要來自實驗數據間的非線性關係，無法使用內插法去求在實驗數據間的門檻值，所以僅能以捨入法查表，大小誤差與亮度誤差分別為正負0.5，因此其總誤差為平方和的開根號。
Contrast 是計算經過濾鏡以及放大倍率後的天空Sky表面亮度與天體Obj表面亮度值的差。請注意我的圖表有時使用（Obj-Sky），有時會使用（Sky-obj），會差個正負號。
資料庫中一些查不到值的PN的表面亮度值由視星等與面積套入公式計算，另，由於小望遠鏡的球狀星團（GC）觀測很接近 extended object，所以也計算了它們的表面亮度值。
濾鏡主要使用OIII， LP2(OIII+Hb)，CLS等，當將它們使用在行星狀星雲、發射星雲上會不同程度降低天空的亮度，合理假設不會影響到星雲因為它們的譜線強度僅集中在極少數幾個波長。
至於倍率/出瞳徑的影響則對於天空與星雲降低的表面亮度值都一樣。
（注意：表面亮度值本身的計算會有差異，不同的來源列出的同一個天體表面亮度值經常不同）
Database parameter description
I have added many features to the spreadsheet , including testing sky brightness, magnification, and filters. I can test visibility based on specific observing conditions, and the spreadsheet will use the test data instead of my own observations to calculate contrast, specifically the Contrast threshold, this is the detectable surface brightness of a target under a specific set of conditions, where if the brightness of the object after magnification (obj. +magnified) is brighter than this threshold, then it is visible.
This contrast threshold theory comes from Blackwell's 1946 experiment on the human eye's contrast threshold. I referred to Roger N. Clark's "Visual Astronomy of the Deep Sky," which may be the first systematic book to apply Blackwell's experimental results to visual observation. I also learned the estimation method for the contrast threshold spreadsheet from the Royal Astronomical Society of Canada.
"Out of size range" indicates that the magnified size exceeds the maximum size of 360' in Blackwell's experiment, and therefore cannot be calculated.
The database and statistical chart show that the contrast threshold has a ±0.7 mpsas error. This error is mainly caused by the non-linear relationship between the experimental data. It is not possible to use interpolation to find the threshold value between the experimental data, so it can only be calculated by truncation.
For some PNs where the surface brightness value is not available, the value is calculated by applying the formula using the apparent magnitude and area. Since observing globular clusters (GC) with small telescopes is similar to observing extended objects, their surface brightness values are also calculated.
'Contrast' is the difference between the surface brightness values of the sky and celestial objects after passing through a filter and being magnified.Please note that the chart sometimes uses (Obj-Sky) and sometimes uses (Sky-Obj), which may result in a difference in the positive or negative sign.
Filters mainly used include OIII, LP2 (OIII+Hb), and CLS, which reduce the brightness of the sky to varying degrees. It is reasonable to assume that it will not affect the emission and planetary nebulae because their spectral line intensity is only concentrated in those few wavelengths.
(圖表 6) 資料庫中所有眼視記錄的天體
（圖表 7）
有面積天體的眼視觀測
觀測時目鏡中的天空表面亮度
觀察以目鏡視野內的天空背景亮度與天體放大後的天體大小（短軸或半光度半徑）觀測數據製作的統計表 (圖6)，它很有趣，明顯的突出了天體的特性。
首先，這個表的上半部是使用高倍率才會到達的天空暗度，因為鞍部的天空暗度平均約在19.5/20 mpsas(南/北)，最暗並未超過20.5（除了十年一遇的一次21），是典型的Bortle 5等級的夜空。因此，其樣本落在表的上半部23~26的表面亮度表示經過倍率與濾鏡的效果將天空亮度降了 3.5到 6.5個星等不等 [若以一般成年人眼的瞳孔大小 6~7mm 計算，大約倍率拉高到目鏡出瞳徑剩下1mm時天空表面亮度約降了4個星等，即原來的SQM20的天空在目鏡中將會變成24的暗度（＊）。出瞳徑1mm即等於使用20公分口徑望遠鏡的200倍，10公分口徑的100倍]。
圖表顯示在目前鞍部三百個天體觀測中觀測時目鏡內的天空表面亮度的最大值是在觀測M57時的 26.27 mpsas。（天空亮度降至比25大（暗）的多半都是在觀察行星狀星雲時，其他主要還是集中在20~25 mpsas之間）
觀測時出瞳徑與降低的表面亮度值的關係（假設人眼瞳孔為7mm時）：
＊若鞍部的天空亮暗度達到SQM20時，當觀測使用出瞳徑在3以下時，目鏡視野內的天空暗度已經超越21.8，也就是金級暗空的裸眼天空表面亮度。（出瞳徑1以上仍算是舒適的觀測條件）
也因此很容易可以說明，為何 圖表7 中當天體暗度達23以上時，使用的出瞳徑都在1.5mm以上 (圖7)，因為當出瞳徑縮到1mm時約會降4個星等的暗度，原來表面亮度為23mpsas的天體將只剩27，天體本身就已經過暗到看不見，也不用談論什麼與天空的對比了。[唯其中有兩個離群較遠的樣本天體表面亮度在23.1然而僅使用0.4mm多的出瞳徑，一個是星團另一個是中央有明亮的WR星，屏除包括他們的三個樣本（這也表示大多數的表面亮度值相當可靠），表面亮度比22暗者使用的出瞳徑都在1mm以上。]
繼續觀察圖表6 ，左上角都是PN行星狀星雲，在放大到這這麼高倍尺寸還如此小、且還（輕易）看得到的，八九不離十都是小行星狀星雲，並不意外（亦可參考圖10）。
而在圖表6的右側，疏散星團分佈非常廣，從低倍到高倍接近人眼的極限，原因是疏散星團的觀測幾乎就是以望遠鏡的極限星等所及，可以放大到極限星等或讓星團充滿整個視野，右下方是些較大的星團，所以在倍率不高（天空表面亮度並沒有降或至少降不多）的情況下尺寸即達到很高的數值，3000’ 即50度，差不多就將要填滿70度目鏡視野。
絕大多數的星系都不大，資料顯示除了M31與M33以外，觀測時放大後的視大小皆在 900 arcmin以下，星系主要佔據在表的中央在天空暗度約20~23間，而其適當倍率主要在出瞳徑1.5至4之間。
要特別說明的是，只有在使用望遠鏡時你的眼睛的適暗性 (dark adaptation)才能超過無光害夜空的 22 mag/arcsec^2 (mpsas)的亮度，因為在望遠鏡放大倍率的視野才能將暗度降超過22這個一般暗空極限值，當你眼睛適應了目鏡視野內的天空暗度，將倍率推向極限，幾乎都可以達到26 mpsas。[人眼視桿細胞即暗視覺（scotopic ）可感應的流明極限 （10＾−6 cd/m2 ，換算表面亮度為 27.583559 mag/arcsec^2），也有其他來源稱極限為27 mag/arcsec^2，以上資料尚待進一步查證。]
根據適暗性也可以說明，為何旁人不一定能看到你目鏡視野裡的天體，尤其若在此之前他一直只是以裸眼觀察星空，他的眼睛只適應了裸眼極限星等的暗度。
As for the effect of magnification/exit pupil diameter, it reduces the surface brightness value of celestial objects and nebulae in the same way.
(Note: There may be errors in calculating the surface brightness value itself, and the same surface brightness value for the same celestial object listed by different sources often differ.)
First, look into the statistical table 'the brightness of the sky background within the eyepiece's field of view and the apparent size (short axis) of the object after magnification' (pic. 6), It is interesting and clearly highlights the characteristics of objects. The upper half of the table represents the sky darkness that can only be achieved with high magnification, as the average sky darkness at the 45-degree elevation angle is about 19.5/20 (South/North), while the surface brightness in the range of 23-26 in the upper half of the table indicates that the sky brightness has been reduced by 3.5 to 6.5 magnitudes due to the effects of magnification and filters.
With the pupil size of an adult's eye (6-7mm), the sky surface brightness is reduced by approximately 4 magnitudes when the magnification is increased to the point where the exit pupil diameter of the telescope is only 1mm, which is equivalent to using a 20 cm aperture telescope at 200 times magnification or a 10 cm aperture telescope at 100 times magnification.
It is also easy to explain why the exit pupil used is above 1.5mm when the darkness of the celestial body reaches 23 or more (pic. 7), because reducing the exit pupil to around 1mm will result in a decrease in brightness of about 4 magnitudes.When the celestial object's surface brightness drops below 27 MPSAS, it is already considered extremely faint.
two outlier sample objects have a surface brightness of 23.1 but use only a 0.4mm exit pupil diameter. One is a star cluster and the other is a central WR star with high brightness. Excluding these three samples, all other objects with a surface brightness darker than 22 use an exit pupil diameter of at least 1mm.
A statistical table provides valuable insights into the characteristics of celestial objects, such as the surface brightness and size after magnification. In the upper left corner of the chart (pic. 6), most of the objects are planetary nebulae, which are still visible at such high magnifications. On the right side of the chart, there is a wide distribution of open clusters, from low to high magnifications approaching the limit of human vision. Because the observation of open clusters is almost limited only by the limiting magnitude of the telescope, and they can be magnified to the limit or fill the entire field of view. The objects in the lower right corner are obviously larger clusters, so their sizes reach high values even at low magnifications where the sky brightness has not decreased much or at all, up to 3000' or 50 degrees, almost filling the 70-degree field of view of the telescope.
Most of the galaxies are not large, and the observation data show that they mainly occupy the central area of the table with a sky darkness of about 20-23, and their appropriate magnification can be seen primarily between the 1.5 and 4mm exit pupil diameter.
It should be noted that only when using a telescope can your eyes' dark adaptation exceed the brightness of the dark sky without light pollution, which is 22 mag/arcsec2, because the field of view of the eyepiece at magnification can reduce the darkness beyond the general limit of 22.
When your eyes adapt to the sky darkness within the telescope's field of view and the magnification is pushed to the limit, almost 26 can be achieved .
(the scotopic vision of the human eye, which is the sensitivity of the rod cells to light, can detect a luminous flux limit of 10^-6 cd/m2, which corresponds to a surface brightness of 27.583559 mag/arcsec2.)
Based on the concept of dark adaptation, it can also explain why others may not be able to see the objects in your telescope's field of view, especially if they have only been observing the night sky with their naked eyes before, their eyes only adapted to the darkness of the sky.
觀測時目鏡中的天體表面亮度與視大小，以及天空與天體的亮度對比
（圖9）
(圖10)
圖9與圖10 大致上顯示了在觀測時的目鏡中的天體的暗度與天體大小成正比關係，短徑最為明顯 (其中 b 是天體的短徑，Re是天體的半光度半徑 half-light radius，在鞍部以小望遠鏡眼視星系與球狀星團時所見的範圍極接近這個範圍，遠小於公認的天體大小)。尤其有幾個天體亮度與天空亮度成極大負對比的（sky-obj, 圖中負對比表示視野中天體比天空表面亮度還暗），都在分佈的上緣。
(但有兩個天體例外，ARO174 與Jones-Emberson 1 在觀測時的目鏡內的天體暗度經計算後超過28mpsas ，尚待近一步確認數據，暫時先不放入圖表中)
這樣的趨勢約一直到天體尺寸放大至2度 (120arcmin)以上逐漸趨緩，至30度之後似開始有反轉的傾向，意即大部份天體放大至如此大尺吋時已達眼視可見的暗度極限。
另，因為這三百個天體素描是並非根據理論計算門檻最佳倍率去觀測的，而是在觀測後才計算數據去與理論門檻比較，因此圖10也直接否定了關於深空天體的觀測應使用低倍率的都市傳說，因為如果黯淡的天體應用越低倍率才看得到，那麼這張圖表的天體分佈走勢應該要從左上到右下才是。
The sample generally demonstrates a proportional relationship between the brightness and size of celestial objects observed through magnifying telescopes, with the effect being most pronounced for the shorter diameters (Figure 9, 10). In particular, several objects exhibit a significant negative contrast with the brightness of the sky (negative contrast indicates that the objects appear darker than the surface brightness of the sky in the field of view), and these objects are primarily located along the upper edge of the distribution. This trend continues until the objects reach a size larger than 2 degrees (120 arcminutes), at which point it gradually diminishes. Beyond 30 degrees, there appears to be a tendency for reversal, indicating that most objects have reached the limit of visual darkness when magnified to such large sizes. The distribution chart of magnified object brightness and apparent size (Power * b) in Figure 10 reveals some observations regarding the variation of the optimum magnified visual angle (OMVA).
Furthermore, because these 300 sketches were not observed based on the threshold theoretically calculated optimal magnification, but rather, the data was collected after the observations to compare with the theoretical threshold. Therefore, Figure 10 directly refutes the urban legend that low magnification should be used for observing deep-sky objects. If faint objects were only visible at lower magnifications, then the distribution trend of objects in this chart should be from the top-left to the bottom-right.
(圖11)
大致可看出天體亮度比天空暗越多的天體尺吋需要越大才能被看見 (反之，天體比天空明亮越多，觀測天體尺寸所需越小)，這個趨勢在300'以內很明顯。 It can be observed that celestial objects with a darker brightness compared to the sky require larger sizes to be visible (conversely, the brighter the celestial object compared to the sky, the smaller the required observation size). This trend is particularly evident within 300 arcminutes.
（圖12）
如果我們檢視“對比與使用倍率”的圖表，請看分佈的樣本的下緣，在80倍以下大致上呈現對比越大則使用倍率越大的趨勢。if we examine the chart of "Contrast versus Magnification," please note the lower edge of the distribution of the samples, which roughly shows a trend where larger contrasts correspond to higher magnifications below 80x (Figure 12).
備註：
H. Richard Blackwell (1946) 的論文《人眼的對比門檻值》是一項探討了人眼可以辨識的最小對比度。該研究是通過要求一組受試者識別出一個小圓形的測試斑塊的存在，該測試斑塊被投影到一個更大的均勻背景上。然後改變測試斑塊的對比度，並測量受試者辨識出它的能力。
研究結果表明，人眼的對比門檻值取決於背景的亮度。當背景非常明亮時，對比門檻值很低。這意味著人眼即使在背景明亮時也能探測到很小的對比度差異。然而，當背景非常暗時，對比門檻值很高。此則意味著人眼在背景暗時更難探測到小對比度差異。
研究還表明，人眼的對比門檻值取決於測試斑塊的大小。當測試斑塊很小時，對比門檻值很高。表明人眼更容易辨識出較大的斑塊。
Roger N. Clark在他的“Visual Astronomy of the Deep Sky”一書中將此實驗結果應用在眼視觀測有面積的深空天體上。
PS.
The paper "Contrast Thresholds of the Human Eye" by H. Richard Blackwell (1946) is a study of the minimum contrast that the human eye can detect. The study was conducted by asking a group of human subjects to identify the presence of a small, circular test patch that was projected onto a larger, uniform field. The contrast of the test patch was varied, and the subjects' ability to detect it was measured.
The results of the study showed that the contrast threshold of the human eye is a function of the brightness of the background field. When the background field is very bright, the contrast threshold is low. This means that the human eye can detect even small differences in contrast when the background is bright. However, when the background field is very dark, the contrast threshold is high. This means that the human eye has more difficulty detecting small differences in contrast when the background is dark.
The study also showed that the contrast threshold of the human eye is a function of the size of the test patch. When the test patch is small, the contrast threshold is high. This means that the human eye has more difficulty detecting small test patches than large test patches.
In his book "Visual Astronomy of the Deep Sky," Roger N. Clark applies the results of this experiment to the visual observation of extended celestial objects in the night sky.
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星系的眼視觀測
半光度半徑 (half-light radius) 與 Sersic 指數
（圖8）目鏡內的天空亮度與天體亮度對比（Sky - Obj, 正值表示天空的SQM數據較大即天空較暗。負值即表示天體較暗。），以天體類別為橫軸
（星系與球狀星團使用半光徑內平均表面亮度）
可輕易發現這裡觀測的目鏡中的絕大部分的星系的半光徑內平均表面亮度都比天空亮度還暗 (圖8)，少數平均表面亮度低於理論可辨識的門檻，但誤差都在一個星等以內，除了誤差的因素外，這或可表示這幾個星系的核心亮度都還比它的半光徑內平均表面亮度還亮上許多 (一個星系的亮度從中心到外圍可以差上好幾個星等，視Sérsic index數值越高差異越大)，因此得以在望遠鏡中被看到，觀察統計資料中其中有不少中央亮度應超過半光徑內平均亮度2~3等，而查詢測光資料實際上也是如此。
The majority of galaxies observed through the telescope in this study have an average surface brightness within half-light radius that is dimmer than the brightness of the sky (Figure 8). A few of them have an average surface brightness lower than the theoretically detectable threshold, but the errors are within one magnitude. Apart from the factors contributing to these errors, this may indicate that the central brightness of these galaxies is much brighter than the average surface brightness within their half radius. The brightness of a galaxy can vary by several magnitudes from the center to the outskirts, with a larger difference as the Sérsic index value increases. This difference allows them to be visible through the telescope. The observational statistics show that many of these galaxies have central brightness exceeding the average brightness within their half radius by 2 to 3 magnitudes, and this is confirmed by querying the photometric data.
_indices.jpg)
Sersic 指數用來表示一個星系的表面亮度隨著距中心的距離的變化程度。大質量的橢圓星系n普遍在4左右。
我們可以參考經常被引用的J.Kormendy的資料，鄰近的橢圓星系與螺旋星系的中央表面亮度普遍在10~19之間（參考下圖），比鞍部的bortle 5的 夜空還亮。
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（來源：
以下進一步針對星系使用半光徑（effective radius）內平均表面亮度做圖（與之前使用的天體平均表面亮度不同）
Further analysis was conducted specifically for galaxies, using the average surface brightness within the effective radius for charting (different from the average surface brightness used previously).
左邊的紅線可作為min apparent size的參考。Fireworks galaxy (NGC 6946)雖黯淡，但於鞍部在充份適暗下可以看見核心，很適合做為一個極限值的參考。此外，NGC 247也是一個極限的目標。The red line on the left serves as a reference for the minimum apparent size. The Fireworks galaxy (NGC 6946), although faint, exhibits a visible core in the Anbu under sufficiently dark conditions, making it suitable as an extreme reference. Additionally, NGC 247 is also an extreme target for analysis.
NGC 6946
眼視觀測中的對比門檻 Contrast threshold in visual observation
下表是資料庫即 spreadsheet 中所有已有素描眼視觀測的有面積天體中可以推估出理論對比門檻值的部分（約將近170個 extended objects），以目鏡內的表面亮度對理論門檻表面亮度值做圖（星系與球狀星團以半光徑為計算標準）。
門檻值的正負 0.7誤差值（兩個0.5誤差的平方和再開根號）主要來自參考Blackwell實驗數據間的非線性關係，所以在查表時是使用捨入進位，以及表面亮度本身的誤差等。紅線為理論門檻值，綠色線為 +0.7 mpsas的上容許誤差值，再加0.8上去的黑色線是根據實驗Averted vision(側視法) 平均所能增加的極限星等。
從圖表中樣本的落點，以及觀測素描中的紀錄描述，呈現的觀測結果與門檻理論預測相當吻合。
因為這些樣本都是已經觀測素描過的資料，所以依據圖表落在上容許誤差值區域 +0 ~ +0.7 間的天體，可視為在包括透明度等天候條件良好的狀況下並充分適暗得以看見 (可以Averted Vision輔助)，這些天體包括：Messier 98, NGC 1232, NGC 1931, Gamma Cassiopeiae Nebula - IC 59, NGC 1360, NGC 4666, Messier 90, Messier 61, Siamese Twins - NGC 4568, NGC 247, NGC 1386, NGC 4535, NGC 4656, NGC 3593, NGC 4038 - Antennae Galaxies.
而在綠線與黑線間則是在良好的條件下仍必須要使用Averted vision才可看見的天體，這些天體包括：NGC 1300, NGC 3896, NGC 3628, NGC 4312, Markarian's Chain - NGC 4458, Siamese Twins - NGC 4567.
（若將觀測分為三個等級，對比門檻值以上可視為較難等級，而門檻值以下至對門檻值的下容許誤差線即 -0 ~-0.7之間可視為中等難度，低於此線以下的天體則為容易等級。唯須注意，天體的對比門檻值會隨著每次的觀測條件不同而有所變化。會影響對比門檻值的因素包括觀測時使用的望遠鏡口徑、倍率，觀測時天體的仰角，觀測方向天空背景亮度，以及視相主要是天空透明度等。）
The table below represents the part of the theoretical contrast threshold values estimated from all the extended objects in sketching visual observations. It plots the surface brightness in the view of eyepiece against the theoretical contrast threshold surface brightness values (galaxies and globular clusters are calculated using half-light radii as the standard).
The errors in the threshold values mainly come from the non-linear relationship among the reference Blackwell experimental data. Therefore, when consulting the table, rounding is applied, along with errors associated with the surface brightness itself. The red line represents the theoretical threshold value, the green line indicates the data allowance for a 0.7 mpsas error, and the black line, which is further 0.7 mpsas above, represents the maximum magnitude increase achievable using the Averted vision technique based on average experimental results.
The distribution of data points on the chart demonstrates a significant level of agreement between the observed results and the theoretical threshold.
Objects falling within the Positive Torrance Zone are considered more challenging objects to observe. They should be visible under excellent weather conditions, including good transparency and sufficient darkness. These objects include: Messier 98, NGC 1232, NGC 1931, Gamma Cassiopeiae Nebula - IC 59, NGC 1360, NGC 4666, Messier 90, Messier 61, Siamese Twins - NGC 4568, NGC 247, NGC 1386, NGC 4535, NGC 4656, NGC 3593, NGC 4038 - Antennae Galaxies.
Between the green and black lines are objects that are still challenging to observe even under favorable conditions and require the use of the Averted vision technique to be more easily visible. These objects include: NGC 1300, NGC 3896, NGC 3628, NGC 4312, Markarian's Chain - NGC 4458, Siamese Twins - NGC 4567.
If observations are categorized into three levels, those above the threshold value can be considered as the more difficult level, while those in the negative tolerance zone of threshold value (-0 to -0.7) can be classified as medium difficulty. objects below this line are categorized as easy level. However, it should be noted that the threshold value for objects may vary with different observation conditions each time.The factors that affect the contrast threshold include the aperture, magnification, elevation, background brightness, and transparency of the sky.
備註：
1995年 Sandro Lanfranco 與 Godfrey Baldacchino 做了一個關於Averted Vision (側視法)的實驗，實驗顯示，與直視法相比，Averted Vision平均可以增加裸眼極限星等約 0.8等。（因為眼睛中央凹的地方沒有負責暗視覺的視桿細胞 Rod cell，所以離中央稍遠的地方暗視覺敏感度較高。請參考 An Investigation of Limiting Magnitude Determination: A Pilot Study
Objects in Positive Torrance Zone:
NGC 1232
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NGC 1931
IC 59
NGC 1360
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NGC 1360
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NGC 4666
M90
NGC 3373
NGC 247
NGC 1386
NGC 4535
NGC 4038
Objects in Averted Vision zone:
NGC 1300
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NGC 4567
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