Astronomical Seeing

Part 2: Seeing Measurement Methods

ASTRO index page

Throughout the 19th century, visual astronomers communicated their observations of astronomical seeing as a qualitative judgment, recorded in language that combined the physical fact with the astronomer's emotional reaction to the fact. Adjectives such as "glorious," "excellent," "good," "passable," "difficult" or "terrible" were typical; most astronomers had a preferred set of descriptive phrases, or used common terms in idiosyncratic and unsystematic ways.

Often a judgment of "good seeing" was the declaration by an astronomer of his confidence in observations made under familiar conditions. The observational aims of the astronomer and his experience of what was relatively good or bad seeing at his habitual observing site significantly affected his appraisal of turbulence. Commonly, the evaluations made by visiting astronomers differed markedly from the resident observers.

As corrective to that disorderly tradition, several more objective seeing scales were proposed around the turn of the 20th century; some of those have come into common use. I describe the most common seeing scales below, with a few examples of abandoned methods.

Scales are grouped according to the criterion used as the test of seeing — subjective image quality, task specific resolution, star diffraction artifact, double star separation, and CCD light distribution. The issue is what the observer is asked to observe as a sign of the atmospheric turbulence, and the validity of that criterion as a basis for judgment.

The following five issues should be kept in mind:

• The perceived effects of atmospheric turbulence are significantly affected by the aperture of the observing instrument. Turbulence that produces a boiling, inflated star image in large apertures will appear as an oscillating but perfect star image in smaller apertures, and at the extreme as "twinkling" in the smallest aperture we use — the naked eye.

• As discussed in the previous page, atmospheric turbulence varies both in the scale or amplitude of optical distortion and in the energy or frequency of the distortion. This is often described as the contrast between oscillation and scintillation, but often both forms of turbulence are apparent, and one can be much more severe than the other. If a rating scale for atmospheric turbulence combines the two, for example as the rating description "frequent large undulations in the image", it makes the application of that rating ambiguous. If the motions are frequent but small, or infrequent but large, does the description still apply?

• The reliability of a rating scale means the consistent application of the scale both by different observers at the same time and by the same observer across time: presented with exactly the same conditions on two different occasions, an observer will give the same rating as he did previously and his rating will agree with the ratings given by other observers. The validity of a rating scale means that different ratings actually reflect some objective and variable attribute of the atmospheric turbulence. Both attributes must be present in a useful rating system.

• Turbulence becomes more or less troublesome depending on the visual or photometric task and on the magnification or image scale required. To ensure reliability, seeing should always be evaluated by means of a specific optical test using the same reference magnification (at least 20 per centimeter of aperture) or measuring instruments, even when images are quite acceptable at a lower power.

• A long research literature in psychology has confirmed that people cannot reliably use more than about 5 rating intervals when asked to communicate subjective or perceptual judgments. Discriminations more nuanced than that are clouded by random error and "guesstimation".

As we'll see, seeing scales generally emphasize the degree of optical distortion present and minimize or ignore the frequency or time scale of variations in optical quality. In effect, they ask the observer or light sensitive instrument to make a time exposure image of a star, and then rate the quality of that static image. But many astronomers have emphasized that frequency is also important, and recommend rating both attributes.

Subjective Image Quality

The Association of Lunar & Planetary Observers Scale

We start with the seeing scale adopted by or attributed to the ALPO. In its briefest form, this is simply communicated as:

"... a numerical sequence ranging from 0.0 (worst possible seeing) to 10.0 (absolutely perfect seeing)".

Observers adopt the lay culture convention of a 0 to 10 scale ("so how did you like the movie, on a zero to ten scale?") and pick a number that corresponds to their impression of the night's seeing in comparison to their personal experience of seeing across all previous occasions. No other guidance is provided, no consideration is made of aperture or image quality: the observers simply state their reaction to what they see based on what they are used to seeing while doing what they normally do. This is essentially the 19th century approach to measurement, in which the expertise of the individual superseded objective facts and consensus judgment.

Sometimes an attempt is made to salvage the scale by providing verbal descriptions of the image quality. The most detailed wording I can find for the ALPO scale — as one of the scales for reporting atmospheric conditions at the Clear Dark Skies web site — is given below.

1 — Very poor images, impossible to see details or to sketch.
2-3 — Almost continuous distortion with occasional brief good moments.
4-6 — More continuous distortions with short intervals of good seeing.
7-8 — Intervals of perfect seeing with fine scale distortions between.
9-10 — Perfect seeing with steady images at high magnification.

Although this scale combines variations in the amount of distortion (very poor to perfect images) and frequency of distortion (almost continuous to short intervals), these verbal anchors do not resolve the problem of ambiguous interpretation. What constitutes an optically "good" or "poor" image is left to the observer's judgment. There is no specification as to what the observer should look at in order to evaluate seeing, or how that should be connected to the range of numerical ratings. This introduces disagreement between observers in the interpretation of the scale, which makes the scale too dependent on the experience of the rater. As one example: there is a general tendency for novices to give more favorable ratings of seeing than experienced observers — novice observers don't know what they're missing.

A second problem is that the wording emphasizes the temporal structure of the turbulence, specifically the relative proportion or persistence of good versus poor images across an extended period of observing. Not only is image quality left to the observer to define, subjective judgments of time ("continuous", "short", "occasional", etc.) are introduced as well.

A final problem with the generic APLO scale (above) is the suggestion to use decimal values in the rating number ("from 0.0 ... to 10.0"), which effectively inflates the rating scale to 100 rating steps. No human observer is capable of consistently or accurately using that many rating intervals.

The Antoniadi Scale

The Antoniadi scale of seeing was suggested by Greek astronomer Eugène-Michel Antoniadi as a note in the Bulletin de la Société astronomique de France in 1909. It provides a broad characterization of seeing in five levels. In English translation (as given in Norton's Star Atlas, 1998, p.59) the scale is typically reprinted as follows:

I. Perfect seeing, without a quiver.
II. Slight undulations, with moments of calm lasting several seconds.
III. Moderate seeing, with larger air tremors.
IV. Poor seeing, with constant troublesome undulations.
V. Very bad seeing, scarcely allowing the making of a rough sketch.

Note that a rating based on the Antoniadi scale is traditionally reported as a Roman numeral.

The qualitative formulation of this scale, and the quirk of linking it to the opportunity to make a drawing, is consistent with Antoniadi's stature as perhaps the greatest visual areographer of all time. However the scale can be applied equally well to almost any lunar or planetary observation. This rough and ready applicability makes the Antoniadi scale one of the easiest to use.

Emphasis is placed about equally on the frequency or duration of the visible thermal turbulence (from moments to constant) and on the visual size of the distortions (quiver, slight undulation, larger tremor). The observer is asked to equate frequency and visual size as two aspects of the same thing, which (as explained in the introduction above) is not often the case.

The specific visual anchors may also truncate the actual range of ratings. The level "perfect seeing, without a quiver" is so extreme that it will be rarely used, even on nights of otherwise excellent seeing. On the other hand, "very bad seeing" seems to describe turbulence that will discourage any attempt at observations — and any need for a rating scale. Ratings therefore will be routinely confined to the middle three alternatives.

The Mt. Wilson Seeing Scale

I provide this scale as an illustration of seeing scales adopted by a specific observatory but otherwise "not widely adopted by the astronomical community". Developed shortly after the Mt. Wilson observatory became operational in 1909, it is reportedly still posted at the control console of the Mt. Wilson 60 inch telescope, now used exclusively by public viewing groups.

The Mt. Wilson scale has the peculiar feature of correlating subjective, image quality judgments with precise estimates of arcsecond seeing. These were apparently collated in 1922 by A.A. Michelson from records kept at Mt. Wilson that compared the MWO seeing scale with the telescope aperture that would show a diffraction limited star image.

I don't have information about the history of the "modified" and base scales. There are problems with the wording of the verbal anchors (how is nearly motionless different from slight motion?), but presumably the continuous use of the scale by personnel at a single location nurtured a conventional interpretation of the scale and assistance from veterans to new observers in how to apply the scale. This is typical of the diverse operating procedures that formed within different observatories in the late 19th and early 20th centuries.

Task Specific Resolution

A interesting feature of early seeing scales is the variety of visual standards used to anchor the ratings. These were typically task specific.

The most flexible scale was developed by A.E. Douglass and described in passing as part of his studies of atmospheric turbulence. It lacks verbal anchors, and is therefore highly subjective; but it illustrates a focus on task relevant features.

The scale required two ratings, linked directly to the lunar and planetary tasks of (1) visual mapping and sketching of surface detail, and (2) micrometer measurements of disk diameter and feature location. As Douglass explained:

"The most important motions were called 'total confusion' [scintillation] and 'bodily motion' [oscillation]. The first was the width through which the limb was indeterminate; it measured the extinction of fine detail. The other was the swaying motion of the whole planet in the field; which is a decided obstacle in good micrometer work."

Describing in 1895 the effect of passing clouds on the atmosphere, Douglass wrote:

"The effect on the planet is what we should expect, — steady and ill defined before the clouds come on (detail 3, limb 7), usually steady and very badly defined amidst them (detail 2, limb 10), and well defined but in considerable motion after they pass (detail 7, limb 4)."

Many task resolution scales utilize very specific criteria to anchor the visual judgments. Among these are scales based on the appearance of the Galilean satellites of Jupiter or surface details on the Moon — the visibility of craterlets on the floor of Plato or rilles near the crater Aristarchus. As one example of the genre, here is the seeing scale developed by Percival Lowell, areological doyen of the early 20th century, that is based on the visibility of features on Mars:

SCALE ON MARS, 10" TO 18" IN DIAMETER, 24-INCH TELESCOPE

0. Image void of contour or detail.
1. Limb moving, polar caps and dark areas alone recognizable, latter unstable.
2. Limb steady, dark areas tolerably so, uncertain glimpses of canals.
3. Coarser canals as streaks, double canals as very broad ones.
4. Coarser canals evident; double canals suspected.
5. Coast lines absolutely sharp.
6. Oases visible.
7. Finer detail tolerably distinct.
8. Double canals perfectly distinct.
9. All detail approaches steel engraving.
10. Image absolutely steady throughout.

This scale illustrates a common problem, which is an ambguity in the visual criteria across different rating levels. If all double canals are perfectly distinct, how is that different from the appearance of a steel engraving? If coarser canals appear as streaks, then how are they not "evident"? These issues are not troublesome when the scale is conceived and used by a single observer, a relict assumption retained from 19th century practice. In fact, many observers of the era could not see and doubted the existence of canals on Mars — Lowell's scale makes clear that they would hardly be compentent to evaluate seeing!

Because task specific scales anchor observations on a specific feature of the criterion astronomical body, they are highly time limited. Craterlets on the floor of Plato are only visible when the terminator is nearby, and no guidance for the rest of the month when the terminator is located elsewhere. The visibility of surface details on Mars varies greatly from conjunction to opposition, and this has nothing to do with seeing.

A more serious problem is that the ratings from one task scale cannot be equated with the ratings on any other. Does the appearance of double canals on Mars signify better or worse seeing than the appearance of the smallest rilles around the lunar crater Aristarchus? The scales only signify the reliability of observations repeated across time on a single celestial target.

All these difficulties explain why task specific seeing scales are no longer used.

Star Diffraction Artifact

The 18th century English astronomer William Herschel was perhaps the first to understand and describe the importance of instrument cooldown, atmospheric turbulence and zenith angle in visual astronomy. But American astronomer William Henry Pickering, while working in 1891 at the Harvard University observing site in Arequipa, Peru, was apparently the first to develop a scale of seeing based on the detailed appearance of a star diffraction artifact.

Pickering's colleague at Harvard, Andrew Ellicott Douglass, describes Pickering as "the first to intelligently appreciate the great importance of seeking a good atmosphere." Douglass goes on to observe:

"Every astronomer knows that ... the definition does not become superb merely because the atmosphere has become clear and perfectly transparent. ... Most astronomers have become aware of this fact and more correctly judge the seeing by means of the steadiness of the air. This is estimated chiefly from the twinkling of stars."

It's regrettable that tradition has disparaged through neglect the careful and insightful research by Douglass on the validity and interpretation of the star diffraction criterion. His work, published in three papers between 1895 and 1898 (see Further Reading) clearly entitles him to coauthorship of "The Standard Scale". His studies advocated the Standard Scale and for the first time pushed the understanding of astronomical seeing beyond "the twinkling of stars". For those reasons I provide a detailed discussion of the scale development.

The Pickering/Douglass "Standard Scale"

The Standard Scale was frequently used during the first decades of the 20th century by Pickering and Douglass at Harvard University observing sites, by Percival Lowell at Lowell Observatory in Flagstaff, Arizona and (in a revised version) by T.J.J. See in Arizona, Mexico and at the United States Naval Observatories.

The earliest mention of the scale is in an article by William Pickering on "Astronomical possibilities at considerable altitudes" in the Astronomische Nachrichten (No. 3079, 1892), where he describes in passing three rating levels on a "scale of steadiness of seeing":

A scale of steadiness of seeing has been adopted on which 3 indicates that the brighter stars are surrounded by numerous diffraction rings, but that they are broken and impossible to count. 4 indicates that they are complete and may be counted, and that the central point of light is readily separable from the inner ring, — while 5 indicates that each ring is perfect and immovable. As it is impossible to detect any improvement upon the latter condition, I have denominated it as "perfect" in my records. Usually half a dozen rings may be seen about the brighter stars, but when the seeing is "perfect" as many as twelve have been counted around α Centauri. This condition it should be stated has been noted on but two or three occasions this year.

Pickering's innovation is twofold: he transferred the benchmark rating criterion from solar system objects that vary in distance or terminator position to the immutable appearance of stars, and he put attention on the diffraction artifact that appears in every telescope regardless of aperture.

The scale proposed by Pickering quickly underwent further development. The version given by Douglass as a footnote in "The Study of Atmospheric Currents by the Aid of Large Telescopes" (1895, p.3) and in "Atmosphere, Telescope and Observer" (1897, pp. 72-3) was based on his own observations at Arequipa, Harvard, Arizona and Mexico. This version is nearly identical to the "Scale of Seeing" published by Pickering in the Annals of the Harvard College Observatory (Vol. XXXII, 1900, p.120), so the revised scale, if not by Pickering, had his approval. Here is a combination of all three versions:

A STANDARD SCALE OF SEEING

With sufficient power (100 to 150 to the inch) the star image consists of a large central disk and a series of rings.

0 — Disk and diffraction rings in one confused mass, violent motion, image greatly enlarged (for example to twice the diameter of the third ring) and varying in size.
2 — Disk and rings in one confused mass, in constant motion, but showing no increase in size.
4 — Disk well defined, no evidence of rings, excepting as a blur, if lens is accurately centered.
6 — Disk well defined, rings broken into dots and lines but still traceable.
8 — Disk well defined, rings complete but moving.
10 — Disk well defined, rings motionless, image moving in field.
12 — Disk well defined, rings motionless, image motionless in field. Perfect seeing.

There is no longer any mention of "counting rings". The last rating level (12) only appears in the 1897 footnote by Douglass; all other versions delete level 12 and the phrase "image moving in field" in level 10.

Douglass consistently distinguished between "twinkling, steadiness and definition" (oscillation and scintillation), and recommended that "with each number [rating on the Standard Scale] should be given the average amount of bodily motion, thus indicating the effect of air waves too large to otherwise affect the form of the stellar image in a 6-inch telescope."

Despite a common misperception, Douglass later affirmed that Pickering developed his scale while using the 13 inch Clark refractor at Arequipa — as Pickering's first mention of "half a dozen rings" around brighter stars makes clear. Later Pickering described the scale as valid "for apertures over six inches", but Douglass states that the scale "varies for different apertures" and suggests "As nearly all observatories have a 6-inch telescope, or one of about that size, or can diaphragm a larger instrument, I recommend the universal adoption of the above scale and aperture as the standard".

The Douglass Research Program

In his 1895 "Atmosphere, Telescope and Observer", Douglass attributes his interest in atmospheric turbulence to the degredation of planetary viewing caused by descending cold air currents at Arequipa and to demonstrations of thermal turbulence he witnessed during Foucault testing of the 40" Yerkes objective lens. This prompted him to undertake a program of systematic observation and experimentation which led him to conclude that "the atmosphere is a factor of prime importance in the definition exhibited by large telescopes and its study becomes of corresponding consequence."

Douglass described the method of centering the telescope on a bright star, then removing the eyepiece to observe the "fine parallel lines" of shadow and light crossing the illuminated exit pupil. He correctly concluded that atmospheric turbulence was "more likely due directly to its temperature changes than to its rapid 'gust' motion"; that "the slightest change of temperature in the dome or in the telescope tube would be harmful"; that stopping down the aperture of a telescope ameliorated the effect of turbulence by "making it more nearly the same size as the air waves"; and finally that "usually our lenses are much too good for their atmospheres."

He correctly observed that turbulence is produced by multiple currents at different altitudes, frequencies, and lateral speeds, which sometimes combine to produce a "vibrating" confusion in the image. He analyzed turbulence on four dimensions: the continuity or steadiness of the currents, their visual width judged against the entrance window of the telescope, their speed, and their intensity or contrast. And he concluded that the thermal turbulence arose from a variety of sources — "convection currents, ... settling of cold air at night, ... mountains or hills, snow [on the ground], cloud condensations, ... and streams of air at different temperatures."

He attempted to measure the altitude of the turbulence layers. Starting from focus at infinity, by "turning out the eyepiece" (defocusing in the extrafocal direction, through the focal points of objects closer than infinity) and noting the extension e needed to focus the waves. He then applied the object distance formula:

distance D = ƒ_o*(ƒ_o+e)/e

with the cosine of the zenith angle to calculate the altitude of the turbulence. With this method he correctly concluded that lower frequency (slower) turbulence is closer to the ground.

Douglass was perhaps the first to note that seeing "certainly does change markedly with alteration in the aperture of the lens" — where alteration implies that judgments were made by stopping down the aperture of a single large instrument. Stopping down a large aperture, which reduces the size of the aperture in relation to the size of the atmospheric waves and visually increases the size of the diffraction artifact at a constant magnification, was a practice common at the time to counteract poor seeing. Douglass summarized his observations, including observations made side by side with a 6 inch and 24 inch telescope, in a remarkable table that equated the effects of seeing with variations in aperture diameter:

His summary comments in Popular Astronomy (1897) are a noteworthy corrective to the amateur's emphasis on optical quality in visual astronomy:

The result of our own experience in studying planetary detail has been to regard the atmosphere as of the first importance, the energy and the intelligence of the observer as of the second and to put last of all, the instrument, provided it gives a fair amount of light; but we find that the value of the instrument increases in an atmosphere that is reasonably near perfect.

Modern Variations of the Standard Scale

The original Standard Scale is not the one in common use today; it has been revised further by anonymous hands. Verbal criteria have modified and odd numbered rating steps inserted, and the size of a badly distorted star image has been explicitly linked to the arcsecond diameter of the diffraction rings as they appear in a 6 inch aperture.

The version given by the editors of Sky & Telescope as A Scale of Seeing (with clarifications adopted from Sidgwick, p.467) is representative of these modern versions of the Standard Scale:

1 — Airy disk and diffraction rings are blurred together; star image is about twice the diameter of the third diffraction ring (if the ring could be seen); star image 13 arcseconds (13") in diameter.
2 — Airy disk and diffraction rings are blurred together; image occasionally twice the diameter of the third diffraction ring (13").
3 — Airy disk and diffraction rings are blurred together; image about the same diameter as the third ring (6.7"); the central Airy diffraction disk is not visible, but the image is brighter at the center.
4 — The central Airy disk is often visible; short arcs of diffraction rings briefly seen on brighter stars.
5 — Airy disk always visible but is mobile; short arcs of the diffraction rings visible about half the time.
6 — Airy disk always visible though not sharply defined; short arcs of the diffraction rings continuously visible.
7 — Airy disk sometimes sharply defined, and distinct from rings; diffraction rings seen as long arcs or complete circles.
8 — Airy disk always sharply defined; innermost ring seen continuously but always in motion.
9 — Airy disk and innermost diffraction ring are stationary; the outer rings are momentarily stationary.
10 — The complete diffraction pattern is stationary.

This table indicates that the commonly cited "Standard Scale" is adapted from the rating labels Douglass used with a 6 inch instrument. Inspection of the other columns of the table illustrates the increasingly worse seeing — and the relative increase in scintillation over oscillation — that occurs as the astronomer uses larger apertures. Thus, the 13 arsecond diameter is calculated for a 6 inch aperture, and will not be valid for objectives of significantly different diameter (see below).

Sidgwick adds useful verbal categories to the scale: 1 to 3 is considered very poor, 4 to 5 poor, 6 to 7 good, 8 to 9 excellent, and 10 perfect. Of interest is the fact that all consideration of oscillation ("bodily motion" or steadiness) has been expunged. Finally, note that the Standard Scale is always reported as an Arabic numeral.

Application of the Scale

There are seven issues of implementation that are commonly overlooked when the Standard Scale is reproduced or recommended for use:

(1) The aperture of the telescope used must be reported, as a single seeing rating scale produces different rating results when used in telescopes of different apertures.

As Douglass explained, this dependency is related to the average physical width of the atmospheric turbulence cells, as they pass across the column of light projected into the telescope. Cells larger than the aperture produce an effect similar to a mirror tilting back and forth, causing oscillation in the image; cells smaller than half the aperture have the effect of fracturing the image into multiple simultaneous images, producing "speckles" or scintillation.

(2) Because a star diffraction artifact is so small, it is not clearly visible unless the observer uses a high diffraction magnification (a submillimeter exit pupil). Douglass (1895) recommended 100 to 150 to the inch of aperture (= 40 to 60 per centimeter of aperture), which yields an exit pupil of 0.25 to 0.17 mm. Sidgwick recommends a magnification of 60 times the aperture (in inches), an exit pupil of about 0.4 mm.

These recommendations follow from a concern that the observer can easily examine the Airy disk, the diffraction rings and the dark intervals between them (or the dark intervals churning within the speckle pattern). They also follow from the fact that magnification, by itself, only makes the diffraction artifact visually larger; it does not alter the effect of turbulence on the diffraction image. The simpler (and more practical) rule is that the observer must use whatever magnification is necessary to make details of the diffraction artifact clearly visible. The magnification limit has been reached only when the star image is either too faint to be seen clearly or is enlarged so much that its oscillation in the eyepiece field is confusing to the eye.

(3) For telescopes in the aperture range 6" to 12", the diffraction rings should be examined in a unitary (not double) star between visual magnitudes 3 to 6. Pickering recommended a magnitude 1 or 2 star, and Douglass "any bright star", but I find (in a 12 inch aperture) that a star brighter than about magnitude 3 can confuse the eye through glare, and a star fainter than magnitude 6 will not show the full diffraction pattern clearly, especially in moderate to extreme turbulence. This is a suggestion only: the magnitude of an optimal test star will depend on the aperture, viewing conditions and the amount of magnification required to see the diffraction pattern distinctly.

(4) Seeing is a variable aspect of observing; it typically changes from moment to moment within larger variations that extend from early to late in the evening. The variability also increases as the average seeing gets better: seeing in the range 0 to 3 tends to be consistently unpleasant, while seeing that rises above 6 makes subtle changes in the seeing easier to notice.

The Standard Scale should be applied by observing a star's diffraction pattern long enough to get a clear idea of the time averaged seeing conditions. Episodes when the seeing is improved should be weighed against periods when the seeing gets worse, until an average value asserts itself. To represent this variation, Douglass recommends reporting the seeing as a range (seeing 2-5) as well as an average value (seeing 3).

(5) Atmospheric refraction varies with wavelength: a "red" star is refracted less than a "blue" star, and the light from a blue star is slightly more severely affected by thermal turbulence. When estimating seeing, you should limit your observations if possible to stars that appear "white" (spectral type A to G). (The spectral type of all naked eye stars is provided in the Yale Bright Star Catalog.)

(6) Seeing and the refractive power of the atmosphere vary with the zenith distance (90° minus the altitude of the star from the horizon) and with the azimuth of observation. Douglass (1898) advised: "In making the observation the name of the star should be recorded, and also its zenith distance and brightness; ... The zenith distance is almost as important as the seeing itself because the seeing varies rapidly with the distance." It is advisable for consistency to rate the seeing using stars at approximately the same zenith distance, between 20° to 40°, and in the azimuth direction in which observations will be done (for example, the direction of the Moon or a planet, or a constellation of double stars).

Stars should not be observed too close to the zenith, because both the observer's body heat, and thermal currents from the mirror of a reflector, will rise upward into the optical path. A telescope mirror placed at an angle allows convection currents to rise off the mirror to one side, minimizing the optical distortion.

(7) In its original form, the Standard Scale asked the observer to make a rating both of the appearance of the diffraction artifact and of "the average amount of bodily motion, thus indicating the effect of air waves too large to otherwise affect the form of the stellar image in a 6 inch telescope". In other words, optical turbulence typically produces both speckles or scintillation and movement or oscillation of the image; the Standard Scale emphasizes the effects of scintillation, so an oscillation rating is also needed.

No rating scale is offered to record this second judgment. Douglass recommends recording the oscillations "in tenths of an arcsecond" but that is needlessly fussy. A reasonable alternative is to report the lateral oscillations as multiples of the star apparent diameter. In poor seeing the star image can oscillate within an area equal to 3 or more times its own width; in good seeing the Airy disk rarely moves outside the circumference of the third diffraction ring.

A historical aside: in 1926 the French astronomer André-Louis Danjon shortened the scale and calibrated it to star diffraction patterns observed simultaneously through a Mach interferometer and a 16cm refractor; in this form it is sometimes called the Danjon scale (not to be confused with Danjon's scale of lunar eclipses).

Double Star Separation

As seeing worsens, the diffraction rings of the diffraction artifact merge with the Airy disk, the oscillatory displacements produced by high and low frequency turbulence merge, and the star image appears to expand in angular size. These facts have motivated a number of seeing scales based on the ability to resolve double stars of equal magnitude and known separation, since the interval that can be resolved will be equal to the average diameter of the star diffraction disk. This strategy is implicit in the Pickering/Douglass Standard Scale, which equates the worst seeing with star disks that are double the angular width of the third diffraction ring.

The See/Cogshall Double Star Scale

References in the literature around 1900 imply that seeing scales based on double star separations were known and used in the late 19th century, at least as task specific resolution scales by double star astronomers.

One such scale was developed around 1900 by T.J.J. See and Wilbur Cogshall as a revision of the Standard Scale, and used by them while measuring binary stars with the 24 inch Lowell refractor:

0 — Light of the star spread all over the field, or expanding and contracting violently.
1 — Image greatly agitated, expanding and contracting; perhaps on the average 6 arcseconds in diameter (for a 6th magnitude star), rays and fringes from 5 to 10 arcseconds long.
2 — Image blurred, less motion, but numerous short fringes, no possibility of seeing a close unequal companion, say the 11th magnitude and distance 1.5 arcseconds, for a 6th magnitude star.
3 — Image blurred, only slightly agitated but surrounded by short fringes; no sharp definition of the central part, and some faint light still diffused about the image.
4 — Image still blurred, scarely any diffused light or rays, but central disk indistinct.
5 — Central disk fairly distinct, no diffused light, only very short fringes, but these moving constantly.
6 — Central disk distinct, short fringes in gentle motion; easy to see an equal double separated by 0.3 arcseconds.
7 — Central disk sharp, fringes short and almost motionless; easy to see parallel fringes of an equal double separated by 0.25 arcseconds.
8 — Perfect central image; diffraction rings and fringes seen in gentle motion, will separate an equal double at a distance of 0.25 arcseconds.
9 — Diffraction fringes numerous and almost motionless; easy to see the closest double separable by the telescope (unless very unequal).
10 — Diffraction rings and fringes perfect and motionless (never realized for any length of time).

The specific reference at several points to precise angular widths would make this scale convenient for use with telescopes equipped with a filar micrometer. However, it also anticipates the exclusive use of star image diameter in the measurement of atmospheric turbulence.

The Tombaugh/Smith Double Star Scale

In the July 1958 Sky & Telescope the astronomers Clyde Tombaugh and Bradford Smith proposed a seeing scale that used the angular separation of north circumpolar double stars as a visual reference for the amount of star image inflation. In principle the method is straightforward: observe different pairs of double stars, of similar magnitudes but different separations, to identify the closest pair in which the separation between the star disks can be clearly resolved.

Their selection of reference stars (updated to separation measurements from epoch c.2005) included:

Star Const. Mags. PA Sep. STF 2241 AB Dra 4.6, 5.6 16° 30.0" STF 485 AE 6.9, 6.9 305° 17.9" STF 2863 AB 4.5, 6.4 275° 7.9" STF 2948 7.3, 8.6 4° 2.7" STF 2950 AB 6.0, 7.1 280° 1.3" STF 185 AB 6.8, 8.6 9° 1.1" STF 2054 AB 6.2, 7.1 350° 1.0" STF 2118 AB 7.1, 7.3 67° 1.0" STF 460 5.6, 6.3 151° 0.7" STT 52 AB 7.1, 7.4 58° 0.5"

Image Diameter Seeing Quality 50" –4 32" –3 20" –2 13" –1 7.9" 0 5.0" 1 3.2" 2 2.0" 3 1.3" 4 0.79" 5 0.50" 6 0.32" 7 0.20" 8 0.13" 9

The observer examines these stars and uses their separation to measure image inflation: if the apparent disks of two stars just touch, and the stars are separated by 1", then each star image is about 1" in diameter. The observer then refers to the table at right to assign a standardized number to the disk diameter. Inspection shows that each step down in this table represents a roughly 160% increase over the previous angular width. This has the effect of placing greater emphasis on differences in turbulence when the seeing is very good to excellent.

The reasons for this second scale and its unusual metric are unclear, as the angular separation by itself is a direct and sufficient measurement of the turbulence. In addition, the range of ratings is too large — no turbulence short of cyclonic will make a 20 arcsecond separation unresolvable — and the relationship of seeing to star image size varies with star magnitude and star color.

Finally, the diameter of a star diffraction image varies inversely with the telescope aperture: the disk appears twice as large in a 6 inch than in a 12 inch telescope. In my 12 inch SCT, twice the diameter of the third diffraction ring is 2.75 arcseconds, slightly greater than the component separation in either of the epsilon Lyrae binaries. In a 6" the same ring will appear slightly more than 5 arcseconds. These complications are not accommodated in the application of the "Seeing Quality" numbers, which must be based on a standard aperture to be interpretable.

Angular Diameter of Star Image

A bit of thought indicates that the double star method of evaluating seeing is really a workaround: it avoids the need to measure the diameter of a single stellar disk with a micrometer or a high power micrometric eyepiece. But if photometric or photographic methods can be supplied in place of visual estimates, then the need for a reference separation disappears. This is the fundamental justification for direct measurement of the angular diameter of star images by means of a CCD receptor.

CCD Full Width Half Maximum

The effect of atmosphere on time exposure digital astrophotographic images is generally summarized in a metric called either full width half peak (FWHP) or (more commonly) full width half maximum (FWHM).

First, let's describe the optical and statistical basis of the method. All optical images of a "point" light source such as a star produce an image that is in fact a diffraction artifact. This artifact appears due to the wave nature of light, and the fact that overlapping wavefronts produced from edges or tiny apertures reinforce each other where the waves vibrate in unison, and cancel each other where the waves vibrate in opposition. These contrasting effects produce patterns of light and dark in a diffracted image.

In telescopes, the diffraction patters are produced by the circular edge of the aperture stop. The resulting star diffraction artifact has a constant form, a bright central Airy disk surrounded by one or more diffraction rings (diagram below, upper right).

The relative size of this artifact is fixed by the aperture or objective diameter of the telescope, its optical quality, and the wavelength of light: larger apertures and higher quality optics produce a smaller and more concentrated diffraction artifact. But regardless of its angular diameter, the artifact has an invariant form in cross section, which can be characterized by a Gaussian or "normal" curve with a high central peak, strongly sloping sides, and a series of diminishing "foothills" that create the concentric rings (diagram above, left). (Note that the horizontal scale is standardized on the ratio of the wavelength of light λ to the aperture diameter D.)

This curve is not a distribution of light but a distribution of probabilities that any single photon will strike a receptor at a specific place. As the total number of photons gathered by the receptor increases (for example, by increasing the exposure time, or by imaging a brighter star), the distribution becomes more fully represented. However it does not become wider as light accumulates, it only becomes taller. As a result — under ideal conditions — the relative horizontal proportions of the distribution remain constant. This is illustrated by the second graph in the diagram (above, right), which shows there is constant relationship between the measured radius of the artifact and the proportion of light energy the radius contains.

A simple method to make equivalent measures of the Gaussian distributions, regardless of the amount of light energy they contain, is the method of full width half maximum. The peak or maximum value of the distribution (in lumens, ADUs, or any other measure of light energy) is divided in half, and the width of the distribution is measured at this half value. As the diagram (above left) illustrates, this results in the same width measurement for high or bright distributions (yellow) as for low or dim distributions (red).

Unfortunately, atmospheric conditions are typically much less than ideal. As a result, the "point" light source does not appear as a single distribution in a fixed location, but as a rapidly mobile cluster of distributions gathered around the most likely location of the point source. This results in a diffuse star image that is many times the diameter of the source Gaussian distribution (diagram below, left).

However, the saving resource here is a statistical law called the central limit theorem. This states that the average or sum of many different distributions will result in a Gaussian or normal distribution — and that this will occur even if the diverse distributions are not themselves normal distributions or normal distributions of the same height or width. As a result, despite the diffusing effect of atmospheric turbulence, the resulting cluster of momentary, mobile Gaussian curves sums to a larger, stable Gaussian curve, and the FWHM strategy can still be used to describe it.

The second, instrumental aspect of the FWHM method occurs in the CCD sensor and image processing software. Although different tools use different proprietary methods, the basic steps are straightforward (diagram above, right):

• The user selects a sample area to measure, which includes all of the star image and some of the background sky. Alternately, the software calculates values for some or all stars within the image.

• Within the sample area, the software sums the luminance value (analog to digital unit or ADU) of all pixels within each row and column of the sample area, multiplies each sum by the pixel address or CCD coordinate of the x row or y column, adds these products together, then divides this weighted sum of the rows and the weighted sum of the columns by the sum of the total ADU signal. This gives the centroid or geometric mean location of the luminance bump in terms of the pixel x,y coordinates.

• The program finds the single pixel peak ADU value, which is identical with or very close to the centroid. It also finds the "floor" value as the average ADU value of background or empty sky pixels (usually after correcting for individual pixel bias by means of a flat).

• The program calculates the radius distance from the centroid to the center of each pixel in the sample area, and plots at this radius the ADU value of the pixel. The result is a descending curve of values, from the peak value to the floor values, that takes the shape of one half of a Gaussian distribution.

• The program determines the half ADU value, and determines the radius from the centroid that corresponds to this value — either by selecting the single closest pixel value, selecting the average radius within a small range of values above and below the half peak ADU, or by fitting a Gaussian distribution to all the data values, and reading the half peak radius from this fitted curve.

• The half radius is doubled and then multiplied by the CCD image scale to give an arcsecond diameter. For example, if the pixel radius is 2.3, and the image scale is 2 arcseconds per pixel, then the FWHM seeing is 9.2 arcseconds. This step projects the observed FWHM into the true field of the sky, making it independent of aperture and CCD format.

Many technical variations are possible: the "star" can be a laser spot reflected off a high altitude thermal layer; multiple measures can be made by a devoted telescope, and these graphed or averaged over time; measures can be taken at different wavelengths, or by means of rotating different aperture stops over the same large aperture instrument. Many professional observatories have automated long focal length telescopes devoted to the task of making continuous measurements of seeing, and the largest instruments can record seeing as an operational parameter of adaptive optics.

On the downside, many purely mechanical or technical issues can compromise the measurement. These include star images that are so bright or overexposed that they saturate individual pixels and cause spillover into neighboring pixels or antiblooming compensation in the CCD, or stars that are too faint or underexposed to generate a Gaussian profile within the diffuse image; telescope mountings that are not polar aligned; telescope drives that add periodic error; inaccurate manual guide star tracking; an image scale that is undersampled (too many arcseconds per pixel); crowded star fields; background nebulosity or light pollution; glare or flare in the optical path; optics that are poorly collimated; stars that are sampled near the image edge, where optical aberrations will be more prominent; and so on.

Because the CCD measurement is time averaged, this method has the advantage of combining the visually distinct effects of oscillation and scintillation into a single metric of image blur. This eliminates the unreliability introduced by visual observers, who must judgmentally either combine the two effects in a single rating or disentangle them into separate ratings.

One drawback is that there is no simple rule to equate FWHM seeing estimates with the quality of seeing judged visually. The reason visual and CCD based image diameter estimates are not comparable is because a CCD image sums all the seeing distorted variations of the star as a single image, but the eye is able to extract from the seeing distorted variations across time a single underlying pattern. Dave Jurasevich offers the guidance that a 3 arcsecond FWHM estimate very roughly equates to seeing that permits the separation of 6th magnitude stars separated by 1 arcsecond.

The Environment Canada Scale

To conclude, and come full circle, here is a seeing scale adapted from the Environment Canada Seeing Forecasts page. This scale is interesting because, like the MWO scale, it links visual descriptions and arcsecond intervals. I also include an animated graphic that suggests the relative appearance of the star disk at these five levels of turbulence.

This scale is recommended to be used only with a "white" star of a magnitude around 2 or 3, observed at zenith angles of less than 30 degrees and with a high magnification eyepiece (yielding an exit pupil of less than 1.0).

Further Reading

Astronomical Possibilities at considerable altitudes (1892) by William H. Pickering - a report on the positive effect of altitude and dry climate on seeing, and the earliest mention of a "scale of seeing".

"The Study of Atmospheric Currents by the Aid of Large Telescopes, and the Effect of Such Currents on the Quality of the Seeing" by A.E. Douglass. American Meteorological Journal, Vol. 2 (1895), pp. 397-401.

"Atmosphere, Telescope and Observer" by A.E. Douglass. Popular Astronomy (Vol. V, No. 2, 1897, pp. 64-84). - A highly informative and prescient early paper on many aspects of astronomical seeing; a revised and expanded version of "The Study of Atmospheric Currents by the Aid of Large Telescopes" of 1895.

"Atmospheric Conditions Essential to the Best Telescopic Definition" by T.J.J. See. Astronomische Nachrichten, Vol. 144 (August, 1897), pp. 81-86. - this and the previous are among the earliest published studies of atmospheric turbulence.

"Scales of Seeing" by A.E. Douglass. Popular Astronomy (Vol. VI, No. 4, 1898, pp. 193-208). - One of the earliest comparative studies of methods of seeing evaluation, with an explicit description of the "Standard Scale" and alternative seeing scales of the era.

Animation Examples of the Pickering Seeing Scale by Damien Peach.

"A Seeing Scale for Visual Observers" by Clyde Tombaugh & Bradford A. Smith. Sky & Telescope (July, 1958, p. 449).

Eight Decades of Astronomical Seeing Measurements at Mount Wilson Observatory by Scott W. Teare, Laird A. Thompson, M. Colleen Gino & Kirk A. Palmer. Publications of the Astronomical Society of the Pacific (Vol. 112, No. 777, November 2000).

Seeing Forecast for Astronomical Purposes at the Canadian Weather Office of Environment Canada.

Astronomical Seeing, an exceptionally in depth page by Jeffrey Beish.

FWHM and Intrinsic Seeing Quality posted by the Isaac Newton Group of Telescopes.

Astroclimatology of Paranal gives annual average FWHM statistics for seeing at the ESO Paranal observatories.

Last revised 11/26/13 • ©2013 Bruce MacEvoy