dblCalc Double Star Separation Calculator Project Page

A Tribute to Amateur Astronomy

Astronomy is among the fastest growing of personal hobbies and one of the most "universally" appreciated of the sciences. Its roots lie in a rich tradition of amateur scientific endeavour. Indeed many amateurs have contributed to important scientific discoveries and helped catalogue the many denizens of the Night Sky.

Beginning with the discovery of the major satellites of Jupiter by Galileo in the early 17th century, the fact that various celestial bodies have one or more companions validated the notion that the Earth is not the center of a pietistic universe created primarily for the benefit of humankind. The motion of such secondary bodies around a common center with their primaries has also made it possible to determine the mass of the bodies involved. Thus double star systems helped demonstrate that many of the fundamental principles of science can be extended far outside the boundaries of our own Earth and the limits of our own solar system.

Beyond the scientific significance of double star systems in the near cosmos, double stars have played an important role in the inspiration of amateur astronomical observation. What budding astronomer does not recall the thrill of first paired-light falling upon a modest amateur telescope?

It is in the spirit of the richness and wonder of personal observation that that the windows-based program "dblCalc" was created using the C++ programming language by myself and programming colleague Bob Crawford.

What dblCalc Does

In the nineteenth century the Reverend W.R. Dawes developed a simple algorithm for predicting threshold resolution of two closely neighboring stars based on telescopic aperture. His method predicted that a pair of 6th magnitude "green" stars could just be resolved if possessed of an angular separation in arc seconds (1/3600th of a degree) equal to the product of dividing the fixed constant 122 by a given telescopic aperture neasured in millimeters. Dawes' method however was not fully extensible across the full range of telescopic magnitudes, nor did it account for disparities in stellar brightness, seeing conditions, or the presence of any fixed central obstruction in the telescopic light path. It would only be that as these variances were examined in detail the ability to predict more sophisticated resolution behaviors became possible.

Beginning in the year 2000, a collaboration between myself and Cor Berrevoet's based on empirical observations of doubles under a variety of seeing conditions and through various telescope types and apertures plus the advent of modern computer methodologies (curve fitting etc.) allowed for pair resolution parameters to be extended into the above described conditions. These early investigations resulted in a first pass at a double star resolution calculator written in DHTML (javascript math engine plus HTML interface). That program is found at: Double Star Resolution Calculator.

Although the web-based version of the Double Star Calculator has proven popular, it fails in its potential due to one major difficiency - the inability to graphically depict what the observer may actually see at the eyepiece. And it is with that aim in mind that Astro.Geekjoy (the website featuring the calculator) inspired the creation of dblCalc - along with the necessity of creating a windows-based C++ application.

Main dblCalc Screen

Screen Capture of dblCalc Dialog screen.

The dblCalc program is written as a single MFC (Microsoft Foundation Classes) dialog supported by a pair of OS filesystem dialogs and about dialog. The program originated within the Windows-98 OS and was completed on NT-based Windows-2000. The development environment was Version 6 of Microsoft Visual Studio. Skills needed to make this possible for me personally came out of a period of employment during the period 2001 - 2002. But it wasn't until Bob Crawford joined the project - as an expert in low level graphics programming - that the visualization engine used in the current version took form.

The main dblCalc dialog is divided into six element groups: Controls, Telescopic & Double Star Details, Sky Conditions, and Calculation & Visualization Results. These six groups enable the armchair astronomer to specify a wide range of scope types, observing conditions, and double star parameters. In their sum these parameters are used to model the visual behavior of observing a specified pair through the eyepiece of a virtual telescope. In addition to the actual rendering of the results for any given pair a large base of calculation data and resulting images may be stored on the windows filesystem.

dblCalc Controls Group

Labelled buttons in the Controls Section allow the user to access files from the hard drive (OPEN) containing the data needed by dblCalc to evaluate any given double star for resolution by a prescribed telescope under selected sky conditions. Such dblCalc specific data files (.DCD extended) must have been previously created by the user and stored on the hard drive using the SAVE AS pushbutton. The act of saving a DCD file also stores the associated image under the same file name - .BMP extended. That image is located in the same directory as the DCD file and is loaded transparently whenever the associated DCD file is OPENed.

Before a DCD file may be saved it's content must first be inputed using other dblCalc screen elements. In addition the data must be validated using CALCULATE. Calculation also results in the rendering of the double star in the Visualization Results frame.

When dblCalc is first displayed its form elements are pre-populated by data associated with the beautiful Summer/Fall double star Albireo. The rendered image Albireo is also seen. Most amateurs will probably quickly overwrite the telescopic parameters associated with its rendition to represent their own personal telescope. Once this is done it is only necessary to click CALCULATE to see the pair as it would appear through their own instrument. Once this is completed SAVE AS allows the user to store their own version of Albireo in the dblCalc directory where they have unzipped the program. Meanwhile dblCalc also stores the data from the last CALCULATE operation in an initialization file. That file and its associated bitmap image are subsequently loaded the next time dblCalc is run.

Should the user want to avoid problems with cross-pair contamination of data, dblCalc also includes a CLEAR button. Using this button ensures that the user will have to populate every input element with their own data before a calculation will be allowed. Meanwhile it is also possible to recover the last calculated data by pressing RESTORE - should clear be accidentally pressed during dblCalc use. However the data returned will of necessity be the data stored on the last successful calculation.

Of "supreme importance" is the ABOUT button. This button allows the user to keep track of version and source information. It also pays homage to those who collaborated in dblCalcs creation - either by coding (Bob Crawford who wrote the visualization engine), mathematical input (Cor Boerevoets who did the original curve tracing for magnitudinal and central obstruction compensation) or "The Astronomer" (source of personal inspiration).

dblCalc Telescope Details Group

An astronomical telescope is a window through which light may be collected and organized in such a way as to augment the natural visual perception of a human being. LIght is collected by a telescope based on the amount of surface area exposed to the light. The light is then organized by channeling it along a convergent pathway from the area of collection into a much smaller region called the virtual image. The ability of a telescope to accomplish this task successfully depends on a number of factors. But in general telescopes may be classed by archetectural type (refractor/reflector/catadioptic), aperture (diameter of light collecting area) central obstruction (diameter of light shadowing area) and focal length (distance between the light collecting/organizing medium and the quasi-plane upon which the virtual image takes focus). Of these factors - only focal length is not included as a calculation parameter in V1 of dblCalc (although a later version may use this parameter in a variety of ways envisioned but not implemented).

Of the three main parameters the most significant for dblCalc's purposes is telescope aperture (in mm). The aperture of a telescope is fundamentally responsible for collecting the light of the double and organizing it as a virtual image. The act of collecting and organizing light in this way both enhances luminosity and resolution of otherwise imperceptible detail. After aperture, the second most fundamental parameter is the linear diameter of any round obstruction in the light path (exclusive of spider vane supports for instance). The presence of any such obstruction (with great sensitivity to its diameter) determines what percentage of the light collected from a point source (such as a star) will actually end up in the tiny disk that comprises that stars virtual image plus the inevitable diffraction rings or chaotic glow that surronds that image.

Of tertiary importance is a telescopes archetecture. Of the three main types it is an established reality that refractors (at least those commonly available to amateurs) are more efficient in the collection of light. They are also usually free of any central obstruction. Combining these two factors together results in the reality that refractors are somewhat hindered in their ability to resolve ultraclose doubles but advantaged in their ability to resolve fainter doubles and those of disparate magnitudes placed near the first diffraction ring of the brighter of the two stars in the pair (the primary star).

The least effective archetecture for both gathering light and resolving disparate pairs is the catadioptic model. These models have sacrificed somewhat the ability to give high contrast views for the ability to create wide flat fields (a refractor-like quality) and the capacity for ease of transport and setup (a decidely un-refractor-like quality for scopes of comparable apertures).

Between these two in resolution potential is the newtonian reflector model. Such scopes typically have smaller central obstructions than catadioptics and lack the numerous light scattering / absorbing components of the same that cause visible dimming of stellar intensity and contrast. However, newtonians - especially of the type used in most inexpensive models often lack the image quality of similarly apertured catadioptics. And this reality leads us to one final consideration.

For the purposes of calculation dblCalc makes no judegments about the quality of the optics in use. All scopes are assumed diffraction limited plus. However, a good approximation for binning scopes of varying optical quality is either to limit the seeing function (described later) or inflate the central obstruction diameter (even if none is present on the scope!). Thus those dblCalc users who wish to "fine tune" calculations to better match their own scopes optical performance may ultimately input a central obstruction value where none is actually in evidence. (One inexpensive refractor I use needs roughly a 40 percent central obstruction value (35mm in its case) to give dblCalc views comparable to what is seen at the eyepiece.

dblCalc Sky Conditions Group

A telescope however, is not the ONLY window through which the observer may inspect the collected and organized light of distant worlds... In fact most telescopes - of whatever type - will easily outperform most atmospheric conditions in terms of rendering quality views. It is for this reason that input into the Sky Conditions group is essential to get a sense of what can be seen in the Night Sky.

Fortunately there really are only two parameters of note when it comes to the sky (although many others may be postulated). The sky possesses a certain "transmissivity" to light from space. This parameter may be estimated by determining the magnitude of the faintest star just visible to direct inspection by the human eye. However it is less possible to guage our second factor - sky stability - without actually turning a scope on a suitable star and evaluating its appearance. That factor - sky stability - determines how much chaos is added to the image of the pair as light passes through what can often be a turbulent medium.

It is a little appreciated fact that should an observer manage to survive the conditions of space and look upon the sky unaided more than a hundred thousand stars to magnitude 8.0 would be perceptible. On Earth, views from high mountains devoid of excess atmospheric water may allow stars to magnitude 7.5 to be seen in this way. Clearly, the transparency of the sky imposes a limit on what may be resolved through a telescope. However the nature of that limit is only appreciated when faint pairs are observed - and not usually among the more commonly viewed pairs most amateurs pursue. For this reason dblCalc allows the user to specify sky transparency over a brioad range from magnitude 3.5 to 7.5. Experimentation with this parameter can show just how significant this factor is...

Of even greater significance to resolution is sky stability. In general double star observing is typically pursued only when stability is at least six on a scale of ten. What this means practically is that once light forming the virtual image of a primary begins to spill out past the first diffraction ring the aesthtics of double star observing is lost along with the ability to resolve more challenging pairs. It is also important to note that sky stability also has a significant effect on stellar brightness - as well as contrast. So although the eye may be relatively immune to the effects of atmospheric disturbance when it comes to magnitudinal thresholds - the telescope is not...

It is clear then that proper use of dblCalc for predicting resolution and views requires thoughtful input of seeing stability and transparency. For those who lack such expererience, dblCalc makes an excellent tool for gaining insight into atmospheric effects on viewing...

As mentioned earlier sky conditions parameters may also be used to better map against the optical quality of any given scope. Should a scope have pronounced errors in its light collecting elements (roughness) diffraction ring structures may be distorted and photons intended to collect in the airy disk of a star will often spray errantly about giving an effect similar to atmospheric instability. In such cases seeing stability values above 7/10 may never be experienced at the eyepiece.

dblCalc Double Star Group

Although sky conditions do vary with the position a particular double star takes at any given time in the sky (stars may be overhead, low to, or even below the horizon etc.) most of the parameters on the Double Star Detail group are not essential to creating a visualization. Data - such as pair name, Right Ascension, Declination, and Date of Record - are included for archiving purposes only. What does matter to dblCalc are the brightness of the stars (in astronomical magnitudes higher numbers are fainter) and separation (in arc seconds or 3600ths of a degree).

In general most telescopes give best resolution on stars that are 7 magnitudes brighter than the faintest star they can just reveal under the circumstances. Dawes himself selected a pair of 6th magnitude stars for validation of his model based on the understanding that brighter stars often display flashing virtual disks and show somewhat distracting first diffraction rings. In fact it is also true that most stars will only reveal a clean disk when no brighter than 11 magnitudes above the telescopic limiting magnitude and no fainter than 4 magnitudes above that value. Ultimately, the atmosphere itself imposes a limit to successful resolution based on the fact that as aperture increases resolution of atmospheric disturbance also increase. Because of this the signal to noise ratio of image quality drops as aperture approaches 300mms. (Although adaptive optics used in some professional observatories can go along way in extending resolution well beyond this limit. For this reason dblCalc does not allow pair separation input less than .30 arc seconds.)

These realities are reflected in the fact that dblCalc must calculate the limiting telescopic magnitude in order to successfully model double star resolution. It must also be sensitive to sky conditions (as outlined above) to determine the virtual sizes of resolvable stellar (airy) disks. All of this requires input as to the brightness of the stars involved plus the amount of magnification required to resolve them. For this reason it is important to research pair data in advance of dblCalc use in order to achieve verisimilitude of output.

The final two sets of parameters (position angle and pair colors) are not currently factored into dblCalc separation results. A future version may incorporate star color to adjust airy disk sizes (which vary linearly in proportion to wavelength) but currently this parameter is ignored except for the aesthetics of the view. However both color and position angle effect display characteristics. For this reason predetermined star colors are selectable by drop-down list box while position angle may be input as a 0 - 360 degree value using a editable text field. By carefully selecting these parameters a definite sense of uniqueness is given to each doublestar pair. (Please see Gallery of dblCalc Renditions at Astro.Geekjoy.Com.

Please Note: Up-to-date double star data is available via The Bright Star Catalogue of Alcyone Software online.)

dblCalc Calculations Summary Group

Based on all essential parameters input by the user (those described above) dblCalc provides information about the apparent "space" (in arcsecs) between the two stars, the magnification needed to achieve a good view (or separation) and any qualifying comments. This last is particularly important since it is not always possible for the visualization provided by dblCalc to precisely display some of the nuances associated with the pair through that scope and sky conditions. Thus there are occasions when dblCalc may show the presence of a faint star near a primary BUT the secondary may not be perceptible to an observer.

dblCalc Visualization Window

Ultimately the main distinguishing characteristic between dblCalc and its online version is the ability to see the results. And it is those visible results that proves particularly valuable to the observer either as a source of personal inspiration or as a means to prepare for an evening of double-quest. Based on dblCalc's window into things-double many of the subtleties of observation under the Night Sky are made plain. For example - terms such as "airy disk", "apparent separation", "first diffraction ring", "position angle", and "pair coloration" are all given demonstrable reality in the accompanying rendition of tight and disparate double Delta Cygni at left.

But other concepts such as "aperture-dependence", "sky-conditions", and "disparate pair brightness inequalities" may only be explored interactively by actually playing the "what if" game with dblCalc.

Ultimately however, no visualizizer such as dblCalc can actually reproduce the wonder of an evening out with a small scope navigating the celestial highway, taking eye to eyepiece, and soaking up photons originating from the photospheres of paired stars pendent in the inky blackness of space...

dblCalc Auxiliary Dialogs

dblCalc is a free program for the non-commercial use and enjoyment of amateur astronomers and other lovers of the Night Sky. Any commercial use of the program to generate images for publication - outside of personal, non-advertisement-ridden websites and astronomical society newsletters - must be arranged in advance of publication. This last contingency is based on encouraging a new model of economics where wealth is shared wherever it is gained. It is hoped that users of dblCalc will prove generous in supporting the programs further development and in underwriting other simulation software planned for the future. Many new features in dblCalc (such as multiple star system support) may not happen unless subsidized by one or more patrons. To become a patron please contact jeff.

When using dblCalc for any purposes the following label should be included in any html img tag alt="dblCalc rendition of -pair designation- as seen through -such an aperture and scope type- at -such a magnification- and -such an ULM - transparency and - such a #/10 stability- sky.". (Please hover the cursor over the above visualization window to see an example of alt tag implementation.) The importance of so labeling assures the viewer that the image is a rendition and not a photograph. It also acts as a disclaimer concerning whether an observer will get a comparable view of such a double through their own equipment under various atmospheric conditions.

dblCalc uses a standard windows filesystem dialog box to both open a dblCalc data file type (DCD) and save that type. As you may note from the dialog, after download and unzipping, dblCalc should be placed in its own filesystem folder - free of any other program's elements. Since dblCalc is "stand-alone" there is no need to place it in the windows program files folder. No registry entries are made on insertion - in fact no install wizard is required at all. For this reason the user must first create their own dblCalc file folder unzip the program to that location then right click on the resulting executable and create a shortcut. Once the shortcut is created, it can be dragged onto the windows desktop for ease of access.

Of some importance is also to become familiar with the best way to name files for archive purposes. In keeping with the above discussion, a file handle should include pair designation, scope aperture, type, magnification, and seeing conditions in its construction. This facilitates ease of publication once the bmp file generated by dblCalc (and given precisely the same name as the DCD file) is reformated according to personal requirements. (Most dblCalc bmp files convert nicely into ~25k sized full color jpegs for web-use. NOTE: Since dblCalc only outputs bmp image types, the user must provide their own image conversion software to re-format.)

dblCalc Personalization

When first run dblCalc creates a default settings.ini file that stores important parameters associated with how visualizations are seen in the dialog window. These display parameters (shown at right) influence the apparent distance between, size, brightness, and intensity of stars plus background glow. Within reason (+/- 20% of the initial settings) these important display parameters may be modified using the windows notepad application and saved for implementation whenever dblCalc is loaded. In most instances default parameters should suffice to give satisfactory results. (NOTE: It is helpful to view dblCalc renditions with a minimum of glare on the PC display. Some very faint doubles may require low ambient light or screen-shaded conditions.) But before adjusting dblCalc's own settings parameters, it is most important to fine tune the intensity of the monitors screen using the PC's Gamma video control (and possibly the manual controls on the monitor itself). One final concern of equal significance is to be sure that your monitor is set up to display (at minimum) 800 x 600 pixels and 24 bit color!

Parameters associated with dblCalc renditions have been meticulously optimized for a broad range range of telescope types, apertures, stellar brightnesses, and pair separations. The fact that all this data must be displayed in a display region some 299 pixels square makes it impossible to give a completely accurate rendition of all parameters. When two stars are beginning to merge position angle (for instance) is limited to 45 degree increments. Occasionally a secondary may appear to be on a diffraction ring of the primary when this is not actually the case. (Please check the comments textfield after each calculation for specifics.) Sometimes a faint star will appear brighter than it is likely to be. (Again the comments textfield helps here.) Rarely however, will a star be apparent at the eyepiece that is not visible on a properly setup screen. However adaptation of screen display parameters may be useful in better matching what is seen on the screen to a particular scope and observer - that's why the settings feature was created! But in general, it is with great pride that Astro.Geekjoy.Com gives you:

dblCalc!

Round Up the Usual Questions!

"How can I get a copy of dblCalc?"

dblCalc is available for download at Astro.Geekjoy.Com. Filesize is less than 250 Kbytes - so even small pipe (modem connections) downloads should not take long at all.

"What operating systems support dblCalc?"

dblCalc has been run on Windows ME, and Windows 2000. There is no reason why it should not run on XP. There is no version available to run on LINUX or MAC OS. Should an appropriate sponsor step forward (or programming organization) it should be possible to port dblCalc to these and other operating systems...

"How do I Install dblCalc?"

dblCalc is a standalone executable application (.exe). Simply placing the dblCalc executable into a user created file folder and double-clicking on it will cause it to load and run. However, dblCalc includes several image and data file types for specific double stars. These - along with the application itself - are bundled into a zip file for download off the internet at the above URL. Once download is complete unzip the package (using winzip etc.) into any desired self-created directory. Follow this by right-clicking on dblCalc to create a shortcut. Drag the shortcut to the desktop and place it their in order to conveniently run dblCalc. (Please note: An install wizard version of dblCalc may be developed in the future once a sponsor comes forward to fund this upgrade activity.)

"How do I get started using dblCalc?"

As mentioned there there are several dblCalc data (.dcd filetype) files included in your download version of dblCalc. Click the dblCalc Controls Group OPEN button to call up a windows file open dialog. Double-click on any file (such as "albireo-150mmMCT-75x-55ulm-7see.dcd"). This will populate dblCalc input parameter fields with information based on my telescope :>) and better-than-usual seeing conditions. Then simply go into the Telescope Details Group, select your type scope and change the fields to your telescope (or dream telescope) aperture and central obstruction diameter (if any). Once you have your fields setup click on CALCULATE. This will create an image of Albireo as it might be seen through your scope under the same seeing conditions. Once you've calculated, the final step is to click the SAVE AS button and give albireo a new name similar to the naming protocol used above. (Pair name-scope aperture/type-magnification-transparency-seeing.dcd).

"Can I publish the resulting images?"

Sure! As long as you don't make any money from publication - no big deal! But If you make money in anyway say from banner ads on your website or selling T-Shirts etc. - I wanna hear about it! In the ideal capitalist society wealth gained is wealth shared.

One other important aspect of publication is the fact that dblCalc images are so realistic that folks need to know - at minimum - that the image you create is a rendition and not a photo or CCD-image. So you are strongly urged to provide the following alt="" property in your img src= html tag or caption: dblCalc rendition of (pair designation) as seen through a (scope aperture) (scope type) at (magnification)x and (transparency)ULM - (stability)/10 seeing skies..

"How can I become a dblCalc sponsor?"

Say you like dblCalc but would like to see a new feature or enhancement. Just email me and tell me what that enhancement might be. Then we will begin an email dialog to discuss our various roles in implementing it. So say you would like an Installer program developed that automatically creates a desktop shortcut or adds dblCalc to the programs group menu then either you can write it - or I or Bob can. If you don't program then we can talk about you (or your organization) subsidizing the project. Then when the installer is called your name (or organization's name) plus web URL will be displayed on the Installer screen.

"Is there a dblCalc Users Group online?"

Astro.Geekjoy has its own online forum (AstroTalk). A special section of AstroTalk has been setup to support dblCalc. Joining AstroTalk costs nothing but you will need to join to partcicipate. Outside of AstroTalk it is entirely possible that other ad hoc users groups may be formed. We here welcome their establishment and will be happy to work with such groups to mature dblCalc as well as to develop new programs to give you an opportunity to continue your explorations of the heavens through your own personal computer.

Open Issues With the Current Version 1.0.0

"The dblCalc visualization window isn't 'square'!"

Sorry folks, dblCalc was setup to run on windows desktops based on a landscape presentation ratio of 4:3. If the visualization window is "too tall" then the only fix currently available is too resize your desktop to more traditional values. 800x600 is probably too claustrophobic for most users. 1024x768 is better. Personally I'm setup at 1280x1024. Frankly I am not sure what's to be done about the issue. Presumably I can make a settings query on dblCalc boot up then adjust all the settings accordingly - but I am less than inclined to do so. If you simply must retain your current screen size ratios then I could recompile the program to your specifications. It'd take some work but then that screen size ratio would be available to others as well...

"The dblCalc labels are all truncated on my screen!"

dblCalc was compiled using fonts found on my PC. I tried to stay close to spec but some folks just don't have the same truetype fonts that I do. If this is the case then you will see letters "cut off" on the dialog. The fix is for me to go back to a more generic font type (I thought in fact that I had!) Contact me if you have this problem and I'll recompile using the most basic font type possible (system!) and font size (who knows). We can work this one out together.

"My stars don't look like yours - the colors are all off!"

dblCalc needs at minimum 24 bit colors to look right - anything less and all the realism is lost. So like using the windows desktop ->properties->settings->screen resolution function to get a 4:3 screen size ratio try changing the color quality parameter to the highest possible setting.

"The restore control doesn't work like I expected it to!"

The Restore control button causes dblCalc to load the parameters associated with the last calculated values. So if you make a change to an input parameter and want to go back this will only be possible if you ran a calculation using the previous settings.

My thanks to "El Marko" for flagging these issues.