Canon autofocus information
/forum/topic/241524/5

1 2 3 5
6
7 end

kwalsh
Registered: Aug 30, 2005
Total Posts: 1086
Country: United States

Wow, awesome information, can't believe the original thread got "lost". This should be a sticky.

I'll do my tiny bit to try and add info to it and some half-baked theories

My first reaction (which some others had) was, how does it do this open loop? Won't it need to know the absolute focus position? Well, I got out the optics book and a pad and pencil, and guess what it needs to know?

Absolutely squat!!! Doesn't need focal length or aperature or absolute focus postion!!!

First off, you might read Doug Kerr's most excellent little primer on split prism and phase comparison focus (http://doug.kerr.home.att.net/pumpkin/Split_Prism.pdf).

So basically if you make an generic ray trace diagram and do a little geometry and trig you will see that the physical distance the lens must be moved from/towards the film plane to achive focus given an arbitrary subject distance and starting position for the lens is:

E = P / (2*tan(A))

Where E is the distance to move the lens from/towards the film plane (i.e. the current focus Error), P is the offset of the image patterns on the Phase comparator arrays and A is the "look Angle" of the comparator array prisms from the optical axis (this is a constant determined by the shape of the prisms). This equation is *not* a function of: focal length, aperature, subject distance, or absolute positon of the lens from the film/imager plane. It basically says that for any lens the distance to move the lens is linearly proportional to the distance between the image patterns at the comparator. The phase measurements and focus commands can all be relative and the camera really needs to know nothing about the lens. The lens had just better move the amount the camera tells it and that's about it.

There is one place there is a little error in the above equation - it assumes the film plane is what moves. Unless you' ve got a really wierd camera its probably the lens that moves . This changes the lens to subject distance very slightly. This would introduce a small error if you made a big change in focus for a very very close subject (magnifications greater than 1:1). I don't think it's really possible for the camera to even get a phase measurement in this case, it would rack the focus until it got close enough to make a phase measurement and once it was this close the error would still be well within tolerance.

OK, so that was physics and pretty solid (though please jump in if I screwed up).

On to speculation...

Why does it want to know the focal length? Well, the exposure system certainly cares for calculating 1/f hand holding speed. And the flash needs to know how tightly in can focus its light cone. And well it looks nice in the EXIF. But I don't think the autofocus strictly cares. The depth of field exposure mode probably does though!

Why does it want to know the maximum aperature? Probably to tell whether it should auto-focus at all - for most systems if the aperature is smaller than f/5.6 the prisms on the phase comparators will just see black. For the snazy "high precision" models I'm guessing at 2.8 and faster it uses a different set of comparators with prims that have a steeper look angle (and thus can make a more accurate measure of phase, again see Doug's neat article). If the lens is slower than 2.8 the precision comparators will just see black so it won't want to use them. And of course the exposure system really needs to know this. But as far as the autofocus goes, besides deciding what mode and whether to try and focus at all it is probably not strictly necessary either.

And even more speculation...

So why do many third parties stink at focus? I suppose the servos could be garbage, but I wonder if it isn't more to do a little with the optics. In order for the above system to work when you move the focus it should do so in a well behaved linear fashion. For an "ideal" lens this is easy. But some of these really compact long zoom ratio things do some weird stuff. For example, the Sigma 18-125 while apparently parafocal (i.e. if you move the zoom ring the focus distance doesn't change) it does do a neato thing at least at the long end - when you change the *focus* the *focal length* changes - at infinity it is around 121mm and at 50ft it is more like 118mm (again, thanks to Doug Kerr post on dpreview). So something exciting is going on in there and the focus may not behave well in this "open loop" system. In fact, if in the above case the nodal points don't also magically move just right to compensate this would introduce overshoot into Canon's open loop system (e.g. if auto focus started from inifnity to a middle ground subject the command would over shoot and front focus). For reference, Sigma's SLR's apparently use a contrast detection method that is closed loop (and slow) - so it probably does a good job on their lenses even if the optics are wierd. So I wonder if Canon lenses are optimized for very well behaved focus so this really fast open loop system is accurate and the third parties sometimes don't? Just a guess!

The other (perhaps more likely explanation) is that the third party lens don't handle the second servo command correctly to fine tune the servo position - that'd also introduce error.

I wonder if everyone elses phase comparison autofocus systems are open loop?

All right, I've blabbed enough. Hopefully some one finds that useful or entertaining... or at least a cure for insomnia.

Again, thanks for the awesome info.

Ken



howgus
Registered: Apr 01, 2005
Total Posts: 210
Country: United States

I noticed a while ago that my 20D center AF sensor seemed to be located just off the edge of the viewfinder square. My method was crude but repeatable, involving a near and far subject boundary. I'm guessing that the easier fix would be to move the viewfinder overlay, rather than the AF sensor array. I wonder if there is play in the overlay, as there was in the split prism viewfinder screen I installed.



kjones1451
Registered: May 27, 2004
Total Posts: 42
Country: United States

In response to 1DS focus points.

I found this earlier in the thread. http://www.pbase.com/chuckwestfall/image/18921329

Hope this helps.



ChrisEOS
Registered: Jul 10, 2005
Total Posts: 245
Country: United States

My 20D consistently front focuses. So are lots of other Canon dSLR's as you can see from this thread:

http://www.photo.net/learn/focustest/

How many of you have tested your focus accuracy on your dSLR?

Am I being too picky?



kwalsh
Registered: Aug 30, 2005
Total Posts: 1086
Country: United States


I just got a XT/350D and it seems to always front focus a little. However, it is well within the specification (i.e. focus point should fall within the depth of focus for an XT). Mine hovers around focusing about 30% of the depth of focus forward. This is really only ever a "problem" with my 50 at 1.8. At first when I measured it I thought I'd send it in for service, but after doing a number of well lit tests and calculating what the "acceptable" range was for Canon's spec I determined that the camera was in fact performing to spec.

So make sure you determine by how much it is front focusing or yeah, you may in fact be too picky.

Oh, and of course try more than one lens. My 50/1.8 is from the early 90's and is clearly more eratic, probably on account of an old servo.

Ken



RDKirk
Registered: Apr 11, 2004
Total Posts: 8477
Country: United States

Absolutely squat!!! Doesn't need focal length or aperature or absolute focus postion!!! The phase measurements and focus commands can all be relative and the camera really needs to know nothing about the lens. The lens had just better move the amount the camera tells it and that's about it.

The camera does need to know the maximum aperture of the lens in order to determine the accuracy tolerance. But you're correct, the lens doesn't need to know anything except where to move.

There is one place there is a little error in the above equation - it assumes the film plane is what moves. Unless you' ve got a really wierd camera its probably the lens that moves .

There was a camera--the Contax AX, I believe--that did indeed move the film plane to autofocus. I suspect the Japanese company making the cameras couldn't get Zeiss to make any autofocus lenses, so they put it in the camera instead. I don't know how they did their measurements.

Why does it want to know the focal length? Well, the exposure system certainly cares for calculating 1/f hand holding speed. And the flash needs to know how tightly in can focus its light cone. And well it looks nice in the EXIF. But I don't think the autofocus strictly cares. The depth of field exposure mode probably does though!

In addition, it does not need to know the focal length to determine the focus accuracy tolerance because (according to Canon in Lens Work III) depth of focus does not change with focal length.

Why does it want to know the maximum aperature? Probably to tell whether it should auto-focus at all - for most systems if the aperature is smaller than f/5.6 the prisms on the phase comparators will just see black. For the snazy "high precision" models I'm guessing at 2.8 and faster it uses a different set of comparators with prims that have a steeper look angle (and thus can make a more accurate measure of phase, again see Doug's neat article). If the lens is slower than 2.8 the precision comparators will just see black so it won't want to use them. And of course the exposure system really needs to know this. But as far as the autofocus goes, besides deciding what mode and whether to try and focus at all it is probably not strictly necessary either.

As I mentioned, it needs maximum aperture to determine depth of focus.

So why do many third parties stink at focus? I suppose the servos could be garbage, but I wonder if it isn't more to do a little with the optics. In order for the above system to work when you move the focus it should do so in a well behaved linear fashion. For an "ideal" lens this is easy. But some of these really compact long zoom ratio things do some weird stuff. For example, the Sigma 18-125 while apparently parafocal (i.e. if you move the zoom ring the focus distance doesn't change) it does do a neato thing at least at the long end - when you change the *focus* the *focal length* changes - at infinity it is around 121mm and at 50ft it is more like 118mm (again, thanks to Doug Kerr post on dpreview).

This is actually common in practically all lenses, though. The focal length is only true when focused at infinity.

The other (perhaps more likely explanation) is that the third party lens don't handle the second servo command correctly to fine tune the servo position - that'd also introduce error.

I think this is more likely. I suspect each 3rd party uses a common (to that company) comm language to their lens drive-control cpus across all their lens mounts, but they use a translator chip specific to each mount. For instance, Tamron's 28-75mm zooms would all have a drive cpu that speaks "Tamron," but the lenses with the Canon mount would have a translator that speaks "Canon" while the lenses with the Nikon mount would have a translator that speaks "Nikon." This would introduce, at the very least, a delay that OEM Canon and Nikon lenses don't have.



jojohohanon
Registered: Jul 28, 2005
Total Posts: 23
Country: N/A

RDKirk wrote:
Tamron's 28-75mm zooms would all have a drive cpu that speaks "Tamron," but the lenses with the Canon mount would have a translator that speaks "Canon" while the lenses with the Nikon mount would have a translator that speaks "Nikon." This would introduce, at the very least, a delay that OEM Canon and Nikon lenses don't have.


I dunno. We're talking electronic speeds: a millisecond, if even that.

However, it's very likely that sigma has only partially reverse-engineered the command language, and miss-understands some commands.

It would be possible for a lens+body manufacturer to encrypt the command language, thus making it _impossible_ to reverse engineer it. The technology is cheap enough, and I'm suprised that the 4/3s consortium didn't do this, forcing sigma to license the spec.



RDKirk
Registered: Apr 11, 2004
Total Posts: 8477
Country: United States

jojohohanon wrote:
RDKirk wrote:
Tamron's 28-75mm zooms would all have a drive cpu that speaks "Tamron," but the lenses with the Canon mount would have a translator that speaks "Canon" while the lenses with the Nikon mount would have a translator that speaks "Nikon." This would introduce, at the very least, a delay that OEM Canon and Nikon lenses don't have.


I dunno. We're talking electronic speeds: a millisecond, if even that.

However, it's very likely that sigma has only partially reverse-engineered the command language, and miss-understands some commands.

It would be possible for a lens+body manufacturer to encrypt the command language, thus making it _impossible_ to reverse engineer it. The technology is cheap enough, and I'm suprised that the 4/3s consortium didn't do this, forcing sigma to license the spec.


Canon has continually said that they have not licensed anyone to produce lenses using their mount. All of the 3rd party companies are reverse engineering.

It's not particularly possible to effectively encrypt something like lens movement commands. First, Canon can't introduce an encryption that would prevent old lenses from communicating with new bodies and vice versa. Second, the action itself is so simple and repeatable that any attempt at encryption would be transparent.

OTOH, even a couple of milliseconds of translation delay could result in a lens not receiving a "stop" command in time after it's been given the command to "rack forward" to find the focus point.



fruitpap
Registered: Dec 04, 2003
Total Posts: 18
Country: Netherlands

RDKirk wrote:
OTOH, even a couple of milliseconds of translation delay could result in a lens not receiving a "stop" command in time after it's been given the command to "rack forward" to find the focus point.


But if I understand the information above correctly, there is no such thing as a stop command; the lens is only told to move a certain distance, or even only to correct a certain phase difference. The AF system in the camera only looks once, and does not check the result while the lens is focussing or afterwards.

Still I do agree that introducing encryption now would be very hard for Canon, because they need to maintain backward compatibility.



RDKirk
Registered: Apr 11, 2004
Total Posts: 8477
Country: United States

But if I understand the information above correctly, there is no such thing as a stop command; the lens is only told to move a certain distance, or even only to correct a certain phase difference. The AF system in the camera only looks once, and does not check the result while the lens is focussing or afterwards.

Still I do agree that introducing encryption now would be very hard for Canon, because they need to maintain backward compatibility.


When the camera's sensor arrays take their bit-directional "look" at the scene, the camera calculates the distance and direction the lens needs to move to resolve the array conflict.

But if the image is so out of focus that the camera can't calculate a focus solution, it commands the lens to rack first all the way forward, then all the way backward. It is apparently "watching" and calculating focus solutions even as this racking is going on, and will stop the lens in mid-rack at the correct focus point. That means one command was sent to "rack" and another command was sent to halt the racking at the correct focus point.

I would agree this is probably not a "stop" command; it's probably the same kind of "move to this point" command the camera would normally give, except that the lens is in motion at the time.

That means there has to be some resolution in the lens of any latency between the point the lens was at when the camera calculated the focus solution, the time it issued the command, and the point the lens reacted to the command. It certainly isn't much time.

When we experience 3rd party lenses doing more "hunting" than OEM lenses in dim light (in which takes the camera longer to calculate the focus solution), my theory is that the lens isn't resolving the latency problem fast enough to obey the "move to this point" command while it's racking.

The OEM lenses don't have this problem, which suggests to me that the 3rd party lenses have a greater latency.



kwalsh
Registered: Aug 30, 2005
Total Posts: 1086
Country: United States

fruitpap wrote:
But if I understand the information above correctly, there is no such thing as a stop command; the lens is only told to move a certain distance, or even only to correct a certain phase difference. The AF system in the camera only looks once, and does not check the result while the lens is focussing or afterwards.


That is correct the lens command is to move a certain distance, not start/stop. Know somebody who had to reverse engineer this. I don't know exactly what the fine tuning commands at the end are (nudges the servo to get it in the right position, but apparently doesn't actually check focus again) - I'd think the lens servo would be able to do this by itself, but apparently not.

Oh, and thanks for the comments on my post RDKirk!

Ken



jojohohanon
Registered: Jul 28, 2005
Total Posts: 23
Country: N/A

RDKirk wrote:
It's not particularly possible to effectively encrypt something like lens movement commands. First, Canon can't introduce an encryption that would prevent old lenses from communicating with new bodies and vice versa. Second, the action itself is so simple and repeatable that any attempt at encryption would be transparent.


Encryption that can't be replayed is a solved problem (search for the replay attack). To be specific: Let's assume the command is just a number between 0 and 99, representing how far to focus. Now, the camera thinks of a random number divisible by 100, adds that to the command, and encrypts the sum. The lens decrypts and ignores all but the last two digits. No two commands will ever be the same.

You're right about backwards compatibility, tho. That's partially why I chose the 4/3s std as my example: a completely new standard.

If canon had wanted to, they could have added additional pins to the EF-S mount: the AF commands could then be sent in the clear via the old pins and encrypted via the new. EF lenses listen to the old pins, EF-S listen to the new. Canon would then be able to release a camera that only had EF-S pin-outs; most likely a consumer one, as few pros would go for that. It would be incompatible with EF lenses (except in MF mode), but work with all EF-S lenses.

Note: I don't think they did that, but they could have, if they had intended to migrate to an incompatible standard over a period of time. Perhaps they considered something like that but decided that it would lose more sales from disgruntled customers than it gained from excluding 3rd party lenses. The 4/3s consortium had no such downside, and could have made some money licensing the spec to 3rd party manufacturers.



RDKirk
Registered: Apr 11, 2004
Total Posts: 8477
Country: United States

Actually, I doubt Canon has spent much time thinking about ways to shut out 3rd party manufacturers.

And the 4/3 standards are open, not licensed--they fully hope that as many 3rd party manufacturers get in on it as possible.



Pondria
Registered: Jan 11, 2002
Total Posts: 11873
Country: United States

What a great thread with full of info including mysteries ! I'd like to contribute.

I had great deal of difficulties to understand the discrepancy between the actual physical diagram of the AF sensors and the conceptual diagram over the view-finder markings.


This image is copyrighted by the owner





This image is copyrighted by the owner




Here are my conclusions:
1. The view-finder makings are "conceptual". The rectangles on the view finder has very little to do with the real sensor size and shape. Only the positions matter.
2. The greatest confusion comes with the word "vertical" and "Horizontal". The Fuziness of the vertical line can be detected only horizontally. Thus, the vertically sensitive sensors are physically horizontal lines. The horizontally sensitive sensors are vertical lines. That's why the view finder markings are opposite in this regard.
3. The "image" formed on the AF sensors are NOT the same real image on the film plane. In the AF beam path, there is a set of lens group called "Secondary image formation lens". I speculated that they are to form the phase signals. So, a fuzzy unfocused line or dot can be extent over large area. Look at the center cross sensor. It comprises actually 8 sensors - 4 blues ones are cross type. 2 additional green ones further enhance the horizontal signal, the 2 red ones activated for F2.8 being able to detect faint vertical signals.


RDKirk
Registered: Apr 11, 2004
Total Posts: 8477
Country: United States

Pondria wrote:
Here are my conclusions:
1. The view-finder makings are "conceptual". The rectangles on the view finder has very little to do with the real sensor size and shape. Only the positions matter.
2. The greatest confusion comes with the word "vertical" and "Horizontal". The Fuziness of the vertical line can be detected only horizontally. Thus, the vertically sensitive sensors are physically horizontal lines. The horizontally sensitive sensors are vertical lines. That's why the view finder markings are opposite in this regard.
3. The "image" formed on the AF sensors are NOT the same real image on the film plane. In the AF beam path, there is a set of lens group called "Secondary image formation lens". I speculated that they are to form the phase signals. So, a fuzzy unfocused line or dot can be extent over large area. Look at the center cross sensor. It comprises actually 8 sensors - 4 blues ones are cross type. 2 additional green ones further enhance the horizontal signal, the 2 red ones activated for F2.8 being able to detect faint vertical signals.


If you go back to my Jul 19, 2005 at 11:09 PM post, I've got an annotated version of the sensor diagram. Each of the AF points marked on the focusing screen represents a pair of pixel arrays on the sensor board. It takes two arrays (an array is a line of pixels) to determine the point of focus because each looks at the light from the opposite angle. The arrays in each pair are oriented in the same direction (horizontally or vertically), in line with each other, and are positioned about as far apart as the length of a single array.

The shape of the AF markings on the screen does correspond with the orientation of the arrays--the vertical rectangles represent vertically oriented arrays and the horizontal rectangles represent horizontally oriented arrays. Like using a split-image rangefinder, you turn the orientation of the focusing aide perpendicular to the line you're focusing on for best results.

The central point, being a "cross-type" sensor, is represented by four sensor arrays (a vertical pair and a horizontal pair), however there is a second pair of vertically oriented arrays (seeing horizontal lines) that are swtiched on when an f2.8 lens is mounted that increases the accuracy of the center sensor.

Notice that the sensor board is smaller and narrower than the actual focusing screen, and there may be lenses or prisms that change the angle of the light as well.



Pondria
Registered: Jan 11, 2002
Total Posts: 11873
Country: United States

Kirk,
To get rid of any confusion in communication, I label the physical sensors and the viewfinder markings. Would you please map the sensors to the corresponding marks ? Thanks !
For example,
1 - A,B,C,D
2 - E, F
3 - H, O
And so on ...


This image is copyrighted by the owner





This image is copyrighted by the owner




Jeff
Registered: Dec 31, 2002
Total Posts: 8662
Country: United States

Homework!



eronald
Registered: Feb 02, 2004
Total Posts: 597
Country: France

Where can that japanese diagram be found ? I want a larger/clearer version to look up the characters.

Edmund



RDKirk
Registered: Apr 11, 2004
Total Posts: 8477
Country: United States

Here is the website:

http://cweb.canon.jp/camera/eosd/20d/catalog/index06.html

Here is my analysis of the sensors. Notice that each of the markings on the focusing screen must correspond with at least two lines of pixels. It also appears that with a "normal precision" array of two lines of pixels, the two lines of pixels are about as far apart as the length of a pixel line.

But the central sensor uses eight pixel lines (four arrays). The blue-coded arrays represent the "normal precision" two lines in each array, with both a vertical and a horizontal array.

The f2.8 "high precision" mode involves an entirely separate set of two arrays (red and green). I don't know if these come into play in addition to the f5.6 set or in place of them. Either would increase precision, as the pixel lines of the horizontally oriented array (red) spreads the lines twice as far apart, which in itself would increase accuracy.



RDKirk
Registered: Apr 11, 2004
Total Posts: 8477
Country: United States

Hey, by the way, you're using a 10D focusing screen diagram, rather than the 20D diamond pattern focusing screen.



Derek_Foo
Registered: Sep 12, 2005
Total Posts: 4
Country: Singapore

Very informative article. Thanks RDKirk for sharing the information and thanks Jeff for keeping the information.



RDKirk
Registered: Apr 11, 2004
Total Posts: 8477
Country: United States

Aha, Canon has recently published a 20d white paper which confirms a couple of points of information to the focusing picture.

1. As we had deduced earlier, the change from normal precision mode to high precision mode is, indeed, a switch function executed when a lens of f2.8 or faster is mounted. From what Chuck Westfall says in the latest Tech Tips on the Digital Journalist website, the camera interrogates the lens for this information even if the lens is mounted while the camera is "asleep"--something else we'd already deduced.

2. Also as we had deduced, the central focusing point contains a total of eight pixel segments.

a. Two pixel segments in line with each other comprise an array. There are two horizontally oriented arrays (detecting vertical details in the scene) and two vertically oriented arrays (detecting horizontal details in the scene).

b. A horizontally oriented array operates with a vertically oriented array as a "cross-type" sensor, so there are two "cross type" sensors represented by the marked square in the center of the focusing screen.

c. One of the cross-type sensors operates constantly at "normal precision" with any lens f5.6 or faster. If a lens is slower than f5.6, this array is switched off. This is not a function of light levels, but a switch function executed when the camera interrogates the lens for its maximum aperture. If a Canon teleconverter is attached, the teleconverter also reports its own factor and the camera takes that into account as well.

d. The other cross-type sensor is the "high precision" sensor, which is switched on when a lens of f2.8 or faster is attached. The vertically oriented array of this cross-type sensor apparently works in conjunction with the vertically oriented array of the "normal precision" cross-type sensor. It's not completely clear to me if this actually enhances precision, speed, or both, nor how the additional data is processed.

e. The horizontally oriented array of the "high precision" cross-type sensor is unique because the pixel segments are set farther apart than any of the other arrays to provide a significantly longer baseline. This definitely increases precision for vertically aligned subject details. It's not clear, though, how the camera integrates this data with the data sent by the horizontally oriented "normal precision" array.



oldsouth
Registered: Jan 06, 2003
Total Posts: 174
Country: United States

Which brings us to one of the earlier questions. Which method is best to focus. Center point and recompose, all point, or select the closest point manually to what we want in focus without recomposing.

If the center point is the most accurate with 2.8 lenses, looks like that would be preferred. But then you get into the angle error like was previously explained.



RDKirk
Registered: Apr 11, 2004
Total Posts: 8477
Country: United States

oldsouth wrote:
Which brings us to one of the earlier questions. Which method is best to focus. Center point and recompose, all point, or select the closest point manually to what we want in focus without recomposing.

If the center point is the most accurate with 2.8 lenses, looks like that would be preferred. But then you get into the angle error like was previously explained.


I and most other old guys have always been using FandRC since forever without a problem on film cameras--or, I should say, with manual focus cameras.

However, we rarely attempted to shoot as much razor-thin depth of field work as you youngsters these days. Whenever I did something like that, I was normally using a plain groundglass focusing screen, setting my composition first and focusing directly on the part of the subject that I wanted sharp--no FandRC. Obviously it was manual focusing.

I believe this issue has raised its head primarily because people are trying to do the same thing with autofocusing, but IMO if you're working with razor-thin depth of field and want the zone of sharpness to fall on a specific plane (like midway the forward eye--differences of only a few millimeters when body sway can be measured in two or three centimeters), you really need to be operating manually and not FandRC. Even body sway (yours or the subject's) is enough to throw off such narrow depth of field, so you'd have to watch closely to shoot at the moment it fell right where you wanted it.

This is a problem similar to that of a target pistol or rifle shooter firing "offhand" (without physical support). It's physically impossible for a human to remain absolutely still without support, so the shooter learns to watch the sights as his natural body sway moves the point of aim over the bullsey, then time his trigger squeeze to fire as the aimpoint is right over the bullseye.

In the same way, when shooting for a razor-thin depth of field, photographers will have to compose, focus manually, and then watch how the zone of focus moves as he and the subject sway natrually, timing the shutter release for when the zone of focus is precisely where the photographer wants it to be.



mtl337
Registered: May 30, 2005
Total Posts: 1
Country: United States

If the precision AF is activated by a switch, wouldn't it be nice if there was a hack that would 'trick' my 20D into activating the cross-type sensor for my f/5.6 or larger aperture lenses ....?

Why does it have to be f/2.8 lenses (besides the effort on Canon's part to force me to purchase $$$ glass)?



1 2 3 5
6
7 end