Fits file re-alignment

Fits file re-alignment

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I would like to re-align an image using a reference image (taken from GAIA). I am aware of the software Koords developed by the Karma team:

Unfortunately, the software crashes (with segmentation fault) everytime I try to add a source in either image. Is there a more up-to-date version of this tool? Or simply a different tool?

Update: Thank you for the responses! I will try to better explain exactly what I am trying to do :)

I have an X-ray image taken from Chandra and a GAIA-Aligned HST image. I know that the pointing for the X-ray image is off by ~.5 arcsec or so. I want to re-align the X-ray image so that any X-ray point sources match their optical counter parts using the GAIA-Aligned HST image as my reference. I hope this helps!

I ended up making my own small code that you can find here:

Essentially, after inputting at least 3 matching target (found by eye in DS9 for example), the program will calculate the mean offset and apply it to the target image. The output is a new fits file of the target image with the proper correction.

SAOImage DS9

What's new in SAOImage DS9 8.2:

  • THEME:
  • Fixed an issue with MacOS prism and catalogs.
  • Fixed an issue with Linux/Windows scale, horz, vert graphs.

SAOImageDS9 is a multi-platform tool, a Tk/Tcl program that enables visualizing astronomical images and analyzing complex FITS data.

In-depth dive in the program's features

With SAOImageDS9 you can easily open new FITS files and start examining the content within minutes. The tool also allows importing arrays, n-dimensional raster data (NRRD), flat-binary raster files (ENVI), and other types of visual elements in the following formats: GIF, TIFF, JPEG, and PNG.

After uploading your content, you have the general viewing panel, plus two smaller windows that allow visualizing the space orientation on the map, respectively, the frame, pixel-like objects (for in-detail lookup).

The tool enables frame adjustment on the map, different zooming in and out (with predefined levels), scale configuration, region focus and selection, or mask, graph, and crosshair parameter adjustments.

A utility with embedded footprint server, plot dialogs support, and a Prism feature

SAOImageDS9 is a powerful utility that offers accessibility, solid performance, and flexible design configuration. For example, when it comes to GUI changes, users can replace the light theme with the dark one, and they also have available controllers for the display of all windows, plots, and dialogs.

Furthermore, the app adds an overlay onto any loaded image. This overlay displays valuable configuration options and choices for filtering, sorting, and registering unique observations (from the catalog dialog's config options). Plus, with the new footprint server, users get increased compatibility with Chandra and Hubble Legacy Archive.

Last but not least, with the help of the built-in Prism feature, you can preview and analyze FITS file structures, examine all the extensions (including the headers and the table data), and generate 2D and histogram plots, straight from your column data.


To summarize, SAOImageDS9 is an excellent choice for anyone interested in conducting in-depth analysis in the astronomical field. A major plus are the following: the tool is free of cost, has rich documentation for understanding where to start learning, and is supported by the astronomical community (which is prolific for quality and assistance).

The FITS file format is the most commonly used file format for astronomical data (astro photos!). It’s also not natively readable by the most common photo editing software suites, which seems like a problem to the beginner, and a bit annoying for advanced astrophotographers. So, let’s talk about FITS, baby. Why do we use it, and how can you convert it to something your normal image processing application can understand? I’m in a funny mood while writing this, I hope it makes a dry topic a little more entertaining.

Defining FITS

The current standard as of this article was defined and finalized in 2008, FITS version 3.0, and it’s used for all kinds of scientific data. FITS is not just an image format! Although, images are what is stored most often in these types of files, you can perceivably store anything you want in a FITS file. Data is data.

What does FITS stand for? (…other than truth and justice for all)

F Flexible: FITS is stretchy, it does whatever you want it to do.

I Image: It’s for images…but not just for images.

T Transport: It’s a container for whatever you want, like image data.

S System: I think they added a fourth letter to make it a naughty word. Or, it’s not just a file. You pick.

OK, cool. But what is it…

Think of FITS as a document, a very accurate written description of an image or other data. One of the really cool things about FITS files is also the fact that there is an ASCII (human-readable) file header (the first few bytes of the file) that can contain pretty much whatever you want.

Want to tell us what camera, temperature, wind speed, GPS coordinates, astronomical coordinates, height, weight, eye color, and middle name of the photographer, or virtually any other fact about the data contained there is to know? Done. FITS can handle that.

The actual image pixel data itself is stored in a 1D, 2D, or 3D multi-dimensional array, and it isn’t compressed. The files are big, but the data is very accurate.

Why do we use FITS instead of camera raw?

Guess what: camera raw files (CR2, NEF, etc.) are compressed! Booooo. But that’s not the only reason FITS files are cooler.

Versioning: it’s backward compatible

One of the reasons it was created in the first place was for archival purposes. The standard used for FITS is important, because each newer version has a mandate to support all older versions. That’s cool.

If I had a dollar for every time I was annoyed about a new “better” version of a file format required by a software update that broke backward compatibility, there wouldn’t be ads on this website and I’d own a small island with no outdoor lights allowed after 8pm within a 500km radius and you’d all want to live there.

Quality matters

In my opinion, it’s also pretty cool to use an image format that supports ANYTHING you throw at it. For example, while Photoshop will support 8-bit and 16-bit TIFF images (and maybe 32-bit now?), I’ve used astronomical image processing applications that will support FITS data up to 64-bits per pixel (BPP), and maybe even higher!

FITS can handle it because there is no real theoretical limit. It just stores a bigger chunk of data for each pixel as you increase the BPP. And if we’ve learned anything so far about why we shoot raw (ALWAYS!), we know that a higher BPP is good stuff for those faint cosmic details. Yes, the file sizes dramatically increase, but so what, space is cheap (…another bad pun).

Some may argue that it’s silly to use any BPP higher than what the camera shoots, and while that is true for the original raw image data, it loses face as soon as we start to manipulate it with post-processing software. While there surely is a BPP limit that our weak human eyes can discern, when teasing out the faintest details with some local contrast, the more the merrier. So, bring it on and use the highest quality image format your CPU can handle without releasing the magic smoke that makes it go.

How to use FITS image files

The problem: your favorite image processing application doesn’t natively support the super-cool FITS images you’ve downloaded from [our website, your friend, Hubble, NASA, aliens].

The solution: The ESO/ESA/NASA FITS Liberator software package!

Because they are super nice, the folks at Hubble distribute, for free, a nice little app to help you view and convert FITS images into more “normal” readable formats, like TIFF. It works on Windows and Mac OSX, but takes a little bit of dinging around to get it installed in the newest OSX versions, it seems.

This image shows the third — and best — version of the popular ESA/ESO/NASA FITS Liberator image processing software.

Also, thanks to Twitter follower @AstroFaris for reminding me that there is another option for Mac OSX users: FITS Preview by Cloudmakers.

However, you’re better off, if you can, using FITS images natively in applications like PixInsight, which is now also using a newer open data format called XSIF (that we aren’t going to talk about right now).

How do you know you can trust me?

So, if you want, read more information about FITS and its history and usage on Wikipedia and the official NASA site.

8SE Imaging (again)

In previous installations of DSO imaging with 8SE I have tried to go for very long exposure times (60s+). Careful balancing, alignment and some tricks with picking appropriate time for imaging were pretty rewarding.

This time I decided to go for short exposures but lots of them. I did initial run with 100 shots and I liked what I saw. Weather cooperated two nights in a row and I took 300 last night. The result is above.

Tonight, the weather cooperated once again. I am trying to capture 1000x 10 second images. That should be fun

Edit: comparison of old (2009) and new (2010) method:

Attached Thumbnails

#3 Midnight Dan

Ok Alex, you've GOT to stop this! You're making it VERY difficult to tell people that the 8SE is not an imaging scope!

#4 tvader

#5 Alex Post

The question is: can we close the southern loop with 8SE?

I would say a cautious yes. What is needed is a mosaic, nothing extravagant, just a 2x2 matrix, a couple of hundred samples per cell.

#6 Tel

Excellent once again, Alex ! Pure skill !

Unless it's a closely guarded secret, I think you ought to publish details of this unique talent you have for coaxing such great images from the alt./az mounted 8SE, (if not just to bring tears to my eyes for investing in a sophisticated and expensive GEM for the purpose) ! :bangbangbang:

#7 Peter9

Gosh Alex, abslotuely awesome. Many thanks for posting.

#8 TonyDralle

Careful balancing, alignment and some tricks with picking appropriate time for imaging were pretty rewarding.

Do you credit careful balancing and alignment as components of your success because the tracking was thereby improved?

Also, could you say a little about your sky conditions, i.e., how much light pollution you have?

You are truly an inspiration to those of us who think trying AP with an 8SE isn't worth the effort. Great work!

I concur with Tel's suggestion that you publish details of your work, either here or as a Cloudy Nights article.

#9 Bob Griffiths

In Memoriam - R.I.P. (1943-2016)

I still say you CHEAT. You have to be, I know you are. LOL

Please do not take up drag racing with your family car. you could be running 8's if you get the kind of results you do out of the 8se for imaging.

#10 Alex Post

Thank you all for comments. I will document my process. Regarding sky conditions: I am right on the boundary of orange and red zones. This is where I am taking pictures since I purchased IDAS LPS filter, based on recommendations of many good people of CN (specifically Samir's comparison charts were helpful Samir's filters for heavy light polution ). I also have a remote site, some 80km from my home that is deep in blue zone. I would say that IDAS filter allows me to do very comparable if not better pictures from light polluted site. I am yet to try this filter from the blue zone.

Picture below was taken at midnight facing (south) away from red zone at ISO1600 2 seconds, half moon was rising to the left (east). Orange glow at the horizon is from another red zone south of my home location.

M42 images were taken between 19:00 and 23:00 local time. First images were taken with M42 being about 42 degrees above horizon and last images about 14 degrees above horizon.

I did not make it to 1000 images last night. I finished at 780 with camera battery flashing low. 582 were selected by DSS for final stacking. I am currently on image 201 for stacking The processing has been running on my laptop since 10 hours ago. I would say another 4-6 hours and I'll have results from last night.

As far as alignment and balancing for this latest run - no, I am taking opposite approach: disregarding both.

My reasoning for this experiment was that 10 sec shots should produce very little motion even if tracking is less than perfect. When I document my process you will see that (and how) I spend about 2 minutes for alignment.

In my previous attempts I would spend up to two hours carefully setting up balance and alignment and then go with 60-90 second exposures to minimize tracking errors. An hour or two of the setup was eating into my data collection time, which is precious given poor weather conditions at my location.

What is fits file? How to open fits files?

File type specification:

Graphics file type

The fits file extension is used for Flexible Image Transport System format, a most commonly used standard format for images used in astronomy. Historically, magnetic tape was the original storage medium for FITS formats.

FITS is a digital file format used to store, transmit, and manipulate scientific and other images, specially in Astronomy. A major feature of the FITS format is that image metadata is stored in a human-readable ASCII header, so that an interested user can examine the headers to investigate a file of unknown provenance.

FITS is also often used to store non-image data, such as spectra, photon lists, data cubes, or even structured data such as multi-table databases. A FITS file may contain several extensions, and each of these may contain a data object. For example, it is possible to store x-ray and infrared exposures in the same file.

Photoshop for Astronomy: An Introductory Tutorial

Figure 1. The Trifid Nebula Using the Photoshop for Astronomy Tutorial

The July/August 2008 issue of Photoshop User magazine featured as its cover article Photoshop for Astronomy. Subtitled Cosmological Uses of Our Favorite Software, the article provides a brief introduction to using Photoshop to process astronomical images. Written by Dr. Robert Hurt, a visualization scientist of the NASA Spitzer Space Telescope and a member of the FITS Liberator development team, this tutorial provides a brief introduction to:

  • astronomical imaging
  • FITS astronomical image format
  • FITS Liberator Photoshop plug-in
  • using Photoshop and FITS Liberator to create astronomical images.
Astronomical Imaging

For the benefit of those Photoshop users who have not previously worked with astronomical images, the article provided a very brief introduction to the basics of astronomical image processing. None of this would be anything new to anyone with previous experience with astronomical imaging.

FITS Astronomical Image Format

Just as a PSD is a graphics file format for Photoshop, FITS is the standard graphics file format used for astronomical imaging. FITS is an acronym for Flexible Image Transport System. Though not mentioned in the article, it is important to note that there are several varieties of FITS formats not all of which are "photographic" images.

FITS Liberator Photoshop plug-in

FITS Liberator is a Photoshop plug-in that makes it possible for Photoshop to open FITS files. Dr. Hurt nicely makes the analogy between FITS Liberator's ability to open and perform basic processing on FITS (Flexible Image Transport System) files and how Camera RAW files are handled.

To learn more about the most recent version of the FITS Liberator plug-in, see New Version of Photoshop FITS Liberator 2.2 Released

As mentioned previously, not all FITS files are of what one would consider standard visual images. These "other" FITS files can not be opened by the FITS Liberator plug-in. So just because it is a FITS file (generally having a file extension of .FITS) does not mean that the data it contains is a picture.

Using Photoshop and FITS Liberator to create astronomical images.

The method that Dr. Hurt used to combine the separate FITS images is somewhat different than the method I use. For those unfamiliar with astronomical imaging, each FITS file is of an image representing a different portion of the electromagnetic spectrum. As such, the data actually reflects the luminosity of the object in that portion of the spectrum. In order to obtain a color image, multiple grayscale images from different portions of the electromagnetic spectrum must be combined and each assigned a color value.

One difference in our methods is the way in which the images are brought in to Photoshop with the FITS Liberator plug-in. Dr. Hurt used the Linear Stretch function, shown in Figure 2 below. Pay particular attention to the histogram. The same process is repeated for the other two images used.

Figure 2. Photoshop Tutorial FITS Liberator Linear Stretch Import Histogram

When I bring FITS files into Photoshop, I tend to experiment with using different stretch functions and different black and white points. My goal is to bring out the subtle detail of the nebula. Figure 3 illustrates the image as I imported it - using the ArcSinh(x) Stretch function and altering the black and white points. As you can see, there is much more detail present in the nebula. Of course the price paid for this detail is evident when comparing the final images.

Figure 3. Photoshop Tutorial FITS Liberator ArcSinh(x) Stretch Import Histogram

The way in which the processing of the data was done in the tutorial yields an image that has a dark background sky and an intense red central nebula with hints of green. This is largely a result of two factors. First was the FITS Liberator import described above. Secondly, Dr. Hurt used a Color Fill Adjustment Layer with the Layer Blend set to Multiply to colorize the data. The tweaking of the individual Levels Adjustments Layers had minimal impact on the final result. Figure 4 illustrates the layers used to create the final rendition of the Trifid Nebula per the tutorial instructions.

Figure 4. Photoshop Tutorial Trifid Nebula Layers

Contrast this with the version I created. The most important difference was that when using FITS Liberator to import the FITS file, I applied a ArcSinh(x) stretch function. This substantially altered the shape of the individual histograms and emphasized the low level grays of the nebula. This method also results in many more stars showing up. I also used Hue/Saturation Adjustment Layers with a Layer Blend of Normal vs the tutorial's Color Fill Adjustment Layers set to a Layer Blend of Multiply, to colorize the image. I also used some additional layers to whiten the stars and alter the overall color and contrast of the final image. My version containing my layers is shown in Figure 5 below.

Figure 5. My Photoshop Layers for the Trifid Nebula

To clearly show the final images of the Trifid Nebula that were produced by following the tutorial vs using my own methodology, please view the following two images:

As you can see, Dr. Hurt and I started with the exact same data, used the same tools, but came up with very different visual results. It is the ability to begin at the same starting point and finish at entirely different aesthetic destinations that makes working with astronomical data so stimulating.

Astro-visualization specialists have long turned to Photoshop for rendering research data into publication-quality images, but extracting the image data from the FITS format had never been straightforward until the Photoshop FITS Liberator plug-in came along.

Dr. Robert Hurt, Photoshop for Astronomy, July/August 2008,
Photoshop User Magazine.

Fits file re-alignment - Astronomy

The FITS definition allows for multiple extensions inside one FITS file, each extension can have a completely independent dataset inside of it. If you just double click on a multi-extension FITS file or run $ds9 foo.fits , SAO DS9 will only show you the first extension. If you have a multi-extension file containing 2D images, one way to load and switch between the each 2D extension is to take the following steps in the SAO DS9 window: &ldquoFile&rdquo&rarr&rdquoOpen Other&rdquo&rarr&rdquoOpen Multi Ext Cube&rdquo and then choose the Multi extension FITS file in your computer&rsquos file structure.

The method above is a little tedious to do every time you want view a multi-extension FITS file. A different series of steps is also necessary if you the extensions are 3D data cubes. Fortunately SAO DS9 also provides command-line options that you can use to specify a particular behavior. One of those options is -mecube which opens a FITS image as a multi-extension data cube (treating each 2D extension as a slice in a 3D cube). This allows you to flip through the extensions easily while keeping all the settings similar.

Try running $ds9 -mecube foo.fits to see the effect (for example on the output of NoiseChisel). If the file has multiple extensions, a small window will also be opened along with the main ds9 window. This small window allows you to slide through the image extensions of foo.fits . If foo.fits only consists of one extension, then SAO DS9 will open as usual. Just to avoid confusion, note that SAO DS9 does not follow the GNU style of separating long and short options as explained in Arguments and options. In the GNU style, this &lsquolong&rsquo (multi-character) option should have been called like --mecube , but SAO DS9 follows its own conventions.

Recall the -mecube opens each 2D input extension as a slice in 3D. Therefore, when you want to inspect a multi-extension FITS file containing a 3D dataset, the -mecube option is no good any more (it only opens the first slice of the 3D cube in each extension). In that case, we have to use SAO DS9&rsquos -multiframe option to open each extension as a separate frame. Since the input is a 3D dataset, we get the same small window as the 2D case above for scrolling through the 3D slices. We then have to also ask ds9 to match the frames and lock the slices, so for example zooming in one, will also zoom the others.

We can use a script to automatize this process and make work much easier (and save a lot of time) when opening any generic 2D or 3D dataset. After taking the following steps, when you click on a FITS file in your graphic user interface, ds9 will open in the respective 2D or 3D mode when double clicking a FITS file on the graphic user interface, and an executable will also be available to open ds9 similarly on the command-line. Note that the following solution assumes you already have Gnuastro installed (and in particular the Fits program).

Let&rsquos assume that you want to store this script in BINDIR (that is in your PATH environment variable, see Installation directory). [Tip: a good place would be

/.local/bin , just don&rsquot forget to make sure it is in your PATH ]. Using your favorite text editor, put the following script into a file called BINDIR/ds9-multi-ext . You can change the size of the opened ds9 window by changing the 1800x3000 part of the script below.

As described above (also in the comments of the script), if you have opened a multi-extension 2D dataset (image), the &ldquoCube&rdquo window can be used to slide/flip through each extension. But when the input is a 3D data cube, the &ldquoCube&rdquo window will slide/flip through the slices in each extension (a separate 3D dataset). To flip through the extensions (while keeping the slice fixed), click the &ldquoframe&rdquo button on the top row of buttons, then use the last four buttons of the bottom row ("first", "previous", "next" and "last") to change between the extensions.

To run this script, you have to activate its executable flag with this command:

If BINDIR is within your system&rsquos PATH environment variable (see Installation directory), you can now open ds9 conditionally using the script above with this command:

For the graphic user interface, we&rsquoll assume you are using GNOME (the most popular graphic user interface for GNU/Linux systems), version 3. For GNOME 2, see below. You can customize GNOME to open specific files with .desktop files. For each user, they are stored in

/.local/share/applications/ . In case you don&rsquot have the directory, make it your self (with mkdir ). Using your favorite text editor, you can now create

/.local/share/applications/saods9.desktop with the following contents. Just don&rsquot forget to correct BINDIR . If you would also like to have ds9&rsquos logo/icon in GNOME, download it, uncomment the Icon line, and write its address in the value.

The steps above will add SAO DS9 as one of your applications. To make it default, take the following steps (just once is enough). Right click on a FITS file and select Open with other application&rarrView all applications&rarrSAO DS9.

In case you are using GNOME 2 you can take the following steps: right click on a FITS file and choose Properties&rarrOpen With&rarrAdd button. A list of applications will show up, ds9 might already be present in the list, but don&rsquot choose it because it will run with no options. Below the list is an option &ldquoUse a custom command&rdquo. Click on it and write the following command: BINDIR/ds9-multi-ext in the box and click &ldquoAdd&rdquo. Then finally choose the command you just added as the default and click the &ldquoClose&rdquo button.

Ch 28 Test

Muscles are the tissues or fibers that cause movement of body parts or organs.

Tendons are bands of connective tissue that bind the ligaments to muscles.

Twisting or rotational forces

Check distal​ CSM, apply a sling and​ swathe, and transport the patient.

Check distal​ CSM, apply a traction​ splint, and transport the patient.

En route to the hospital

Pull enough traction to give the patient some relief from the pain.

No traction splint applied in the field pulls true​ traction they must pull 20 pounds of countertraction.

A comminuted break is when a bone is broken in only one place.

A greenstick break is an incomplete break in a bone.

Fractured pelvis
Compression fracture of the lumbar or sacral spine

A posterior hip dislocation presents with a bent knee and the foot may hang loose.

Often there is lack of sensation in the limb.

​Pelvis, hip, or knee injury

Injury to the lower third of the leg that would interfere with the ankle hitch

Possible fracture of the cervical spine

Possible fracture of the femur

Bone ends have lacerated the soft tissues and skin from the inside.

The joint capsule has been torn open during a dislocation.

Gently replace protruding bone ends back beneath the skin to prevent further contamination.

Splint an isolated extremity injury before moving the patient to the stretcher.

Explain to the patient that her ankle is fractured and you must splint her ankle to prevent further injury and reduce pain.

Explain to the patient that her ankle is sprained and transport her with her ankle elevated on a pillow and a cold pack applied to the injury.

You can consider its use based on mechanism of injury​ (MOI).

It should not be used unless the patient shows signs of shock.

The lack of a distal pulse could be a signal of a real emergency.

In a knee​ dislocation, the tibia is forced anteriorly or posteriorly in relation to the distal femur.

Another name for manual traction is tension.

Joints are places where bones articulate.

Many musculoskeletal injuries have a grotesque​ appearance, and the EMT cannot be distracted from​ life-threatening conditions by a deformed limb.

Most musculoskeletal injuries are simply splinted and not a life threat to the patient.

it is hard to access distal pulses after application.

it requires three people to apply.

Do not attempt to realign the extremity before splinting.

Use an upper extremity traction splint.

Explain to the patient​ that, because you cannot detect circulation in his​ foot, his leg will most likely have to be amputated above the site of the injury.

Gently attempt to straighten the leg to regain a pulse before splinting.

Provide manual​ in-line stabilization of the cervical spine along with assessment of​ breathing, pulse, and the presence of significant​ hemorrhage apply​ high-concentration oxygen perform a rapid trauma​ exam immobilize to a long​ backboard and check with medical control about the need to splint the forearm injury prior to transport.

Open the​ airway assess​ breathing check the carotid​ pulse splint the forearm​ injury immobilize the patient to a long​ backboard apply​ high-concentration oxygen and transport.


A list of length two, named '$hdr' and '$dat'. '$hdr' contains the header information for the file, whereas '$dat' contains the imaging or binary table data. Both '$hdr' and '$dat' contain a sub-list for each hdu present in the original file.

Each FITS extension containing a binary table (binary tables are never found in the primary FITS HDU) has additional sub-lists within the '$dat' list, named '$meta' and '$table'. These provide the table meta-data and actual table data itself, respectively.

Fits file re-alignment - Astronomy

The FITS file format is the standard data format used in astronomy, endorsed by both NASA and the International Astronomical Union (IAU). For more information about the FITS standard, go to the FITS Web site, .

The FITS file format is designed to store scientific data sets consisting of multidimensional arrays (1-D spectra, 2-D images, or 3-D data cubes) and two-dimensional tables containing rows and columns of data. A data file in FITS format can contain multiple components, each marked by an ASCII text header followed by binary data. The first component in a FITS file is known as the primary , which can be followed by any number of other components, called extensions, in FITS terminology. For a complete list of extensions, see fitsread .

To get information about the contents of a Flexible Image Transport System (FITS) file, use the fitsinfo function. The fitsinfo function returns a structure containing the information about the file and detailed information about the data in the file.

To import data into the MATLAB ® workspace from a Flexible Image Transport System (FITS) file, use the fitsread function. Using this function, you can import the primary data in the file or you can import the data in any of the extensions in the file, such as the Image extension, as shown in this example.

Determine which extensions the FITS file contains, using the fitsinfo function.

The info structure shows that the file contains several extensions including the Binary Table , ASCII Table , and Image extensions.

To read the Primary data in the file, specify the filename as the only argument:

To read any of the extensions in the file, you must specify the name of the extension as an optional parameter. This example reads the Binary Table extension from the FITS file:

Watch the video: Ευθυγράμμιση Αυτοκινήτου-Τι είναι, κάθε πότε πρέπει να γίνεται; Γωνίες κάστερ, κάμπερ και σύγκλισης (February 2023).