REW Alignment tool - Guides or Manual?

lexicon

Member
Thread Starter
Joined
Nov 8, 2018
Messages
37
Hi All
I have just taken a batch of measurements for LCR and sub using REW (using an acoustic timing ref) and am trying to use the new alignment tool to determine the best delays to add to my processor. But I can’t find anything that explains how to use the tool - no manual, no videos or anything. I don’t know what I’m supposed to align on the phase graphs or what the actual process is. Is anyone aware of any training material I can look at or a step by step guide for idiots?

Many thanks
 
Last edited:

John Mulcahy

REW Author
Joined
Apr 3, 2017
Messages
3,039
If you search this forum for Alignment Tool there are a few threads on it, @jtalden has made many helpful posts on alignment in general and more recently on using the alignment tool.
 

lexicon

Member
Thread Starter
Joined
Nov 8, 2018
Messages
37
If you search this forum for Alignment Tool there are a few threads on it, @jtalden has made many helpful posts on alignment in general and more recently on using the alignment tool.
Many thanks John - I will have a look through. There are a lot of phase related issues and tabs on that section that I do not understand.

Basically I am trying to determine why Dirac only sets a 2.87ms delay between sub and mains when the sub already has a fixed latency of 5-6ms (confirmed by SVS).

Your tool seems to be the best option to see whether the Dirac calculated delays are in fact optimal to achieve the best sub/mains integration.

I just need to learn how to use it!
 

jtalden

Senior Member
Joined
May 22, 2017
Messages
427
Location
Arizona, USA
My AV System  
Preamp, Processor or Receiver
Marantz AV7705 Pre/Pro
Main Amp
Rotel RMB-1066 6 chnl P-amp x 2
Additional Amp
Behringer DCX2496 x 2
Universal / Blu-ray / CD Player
OPPO BDP-103 Universal Player
Front Speakers
DIY SEAS H1456/H1212 Spkr x 5
Subwoofers
DIY JBL 2235H 15" SW x 2
Video Display Device
JVC DLA-X790R
Screen
Da-Lite Da-Snap 39105V - 92"
I can help confirm the favorability of the current SW distance setting using the REW alignment tool. A setting that provides strong SPL support in the XO range a favorable one. To do it manually one could just look at the SPL response through the XO range at different SW distance settings using incremental 30 cm changes. That would reduce the number of trial distances needed and still be able to find all the favorable settings. There are often several different distances that provide a favorable setting. This method takes a lot of time and effort.

The REW alignment tool allows us see the impact of SW distances settings virtually saving a lot of time and effort. In order to evaluate the current Dirac EQ and SW distance settings we ideally should have the following measurements.

Setup:
  • Mic at LP
  • Lexicon in stereo mode
  • Current Dirac settings unchanged (XO, EQ, distances...)
  • Current SW settings unchanged
  • REW Acoustic timing mode selected
  • REW Use L main for the reference channel
  • REW sweep range set to 20-20k Hz
Measurements:
  1. FL (alone; SW off)
  2. FR (alone; SW off)
  3. SW (alone; Measure the redirected bass by using FR channel with the FR speaker disconnected)
Given these 3 measurements, I can outline the REW alignment tool steps needed in this case to evaluate the current SW distance settings vs other options for this current setup.
 

lexicon

Member
Thread Starter
Joined
Nov 8, 2018
Messages
37
That’s perfect thank you so much.

I have done all of that according to your suggestions apart from the fact that I had “native” mode selected on the processor. However all other channels other than the one one being measured and the front left (timing ref) were switched off.

The mic was set at the exact point that the first Dirac measurement was taken from although of course the Dirac settings were obtained after an average of another 4 more measurements around that were completed. That may mean that you will need me to repeat this using just that one initial Dirac measurement? Or I could go back into Dirac and see if I can delete the subsequent 4 and recalibrate with just the one.

It may well be that Dirac only uses the first measurement to assess distances/delays anyway though as they emphasize the importance of taking that measurement from a position equidistant between the left and right main speakers and that is indeed what I did.

Exact distances below were measured using a laser.

MLP to mains 9ft 6 inches
MLP to front of sub 8ft 11inches
MLP to rear wall behind sub 10ft 4inches

I took two REW measurements for the sub - one from centre channel (set to 100hz Xover) and one from front right channel (set at 40hz Xover). I wish I had set all the crossovers the same now and can do it all again with say a global 80hz Xover if needed.

Anyway I attach what I have as a starter!

If there is any way to determine the best Xover to choose using that alignment tool then that would obviously be well worth experimenting with.

I'm aware that there will be a good number of people on AV forums who would like a simple easy to understand step by step guide on how to do this using that alignment tool.

Thank you again

Jon
 

Attachments

jtalden

Senior Member
Joined
May 22, 2017
Messages
427
Location
Arizona, USA
My AV System  
Preamp, Processor or Receiver
Marantz AV7705 Pre/Pro
Main Amp
Rotel RMB-1066 6 chnl P-amp x 2
Additional Amp
Behringer DCX2496 x 2
Universal / Blu-ray / CD Player
OPPO BDP-103 Universal Player
Front Speakers
DIY SEAS H1456/H1212 Spkr x 5
Subwoofers
DIY JBL 2235H 15" SW x 2
Video Display Device
JVC DLA-X790R
Screen
Da-Lite Da-Snap 39105V - 92"
I have done all of that according to your suggestions apart from the fact that I had “native” mode selected on the processor. However all other channels other than the one one being measured and the front left (timing ref) were switched off.
I don't know what native mode is, but it appear to have done the job reasonably well. The odd measurement is the final one. The SW redirected bass as measured through the FR channel with a 40 Hz XO is very high in level, but that may just be your preference. It is particularly notable as the CC channel SW measurement with the i00 Hz XO is about 8-10 dB lower. I can still use this data for the needed timing analysis of the 40 Hz XO on the FL, FR. I will just adjust the SW down 7 dB so I is easier to understand in the analysis.
The mic was set at the exact point that the first Dirac measurement was taken from although of course the Dirac settings were obtained after an average of another 4 more measurements around that were completed. That may mean that you will need me to repeat this using just that one initial Dirac measurement? Or I could go back into Dirac and see if I can delete the subsequent 4 and recalibrate with just the one.
No need to change anything for this timing evaluation.
It may well be that Dirac only uses the first measurement to assess distances/delays anyway though as they emphasize the importance of taking that measurement from a position equidistant between the left and right main speakers and that is indeed what I did.
Yes, the others are for the EQ portion of the setup, not the timing.
I took two REW measurements for the sub - one from centre channel (set to 100hz Xover) and one from front right channel (set at 40hz Xover). I wish I had set all the crossovers the same now and can do it all again with say a global 80hz Xover if needed.
They don't need to be the same frequency. Is the CC identical? If not, the timing is a decision about what portion of the frequency range you want to align with the FL and FR. The CC timing is best done after the SW is timed to FL and FR.
If there is any way to determine the best Xover to choose using that alignment tool then that would obviously be well worth experimenting with.
What speakers are you using? There is nothing wrong with the 40 Hz XO if the mains are capable of the needed output down there. The XO should be higher when using typical mains that cannot easily provide the needed SPL there. Most all SWs are ideal for that low frequency work. Let me know if you decide to change the XO. New measurements should be made with the new setting before the analysis is done. I will wait to hear form you.
 

lexicon

Member
Thread Starter
Joined
Nov 8, 2018
Messages
37
I don't know what native mode is, but it appear to have done the job reasonably well. The odd measurement is the final one. The SW redirected bass as measured through the FR channel with a 40 Hz XO is very high in level, but that may just be your preference. It is particularly notable as the CC channel SW measurement with the i00 Hz XO is about 8-10 dB lower. I can still use this data for the needed timing analysis of the 40 Hz XO on the FL, FR. I will just adjust the SW down 7 dB so I is easier to understand in the analysis.

No need to change anything for this timing evaluation.

Yes, the others are for the EQ portion of the setup, not the timing.

They don't need to be the same frequency. Is the CC identical? If not, the timing is a decision about what portion of the frequency range you want to align with the FL and FR. The CC timing is best done after the SW is timed to FL and FR.

What speakers are you using? There is nothing wrong with the 40 Hz XO if the mains are capable of the needed output down there. The XO should be higher when using typical mains that cannot easily provide the needed SPL there. Most all SWs are ideal for that low frequency work. Let me know if you decide to change the XO. New measurements should be made with the new setting before the analysis is done. I will wait to hear form you.
Many thanks that’s hugely informative and perceptive.

Yes I do use a fairly strong bass lift and 7db corresponds with the Harman based curves used which are attached for both speakers and sub. The mains are floor-standing JBL3900s with the port sealed (all my speakers are now run with ports sealed) and can take more bass as a result without any bloat. The centre (and front heights) are Revel S16s mounted in a line above the screen angled down towards the MLP. Rears, backs and the in-ceiling mid top Atmos pair are all smaller/stand mounts so will all require a higher Xover.

As regards the centre timing, if there is a choice I guess it would be to aim to optimise timing for maximum speech clarity.

If it’s just a case of changing all the crossovers to 80hz and remeasuring with REW without having to rerun Dirac I may as well do that tomorrow and send you another REW MDAT so you can advise which you think is best. I am presuming I would not need to rerun Dirac first? If that was the case I would only be able to accurately replicate the first Dirac mic position anyway (which I was careful to record).

Jon
 

Attachments

jtalden

Senior Member
Joined
May 22, 2017
Messages
427
Location
Arizona, USA
My AV System  
Preamp, Processor or Receiver
Marantz AV7705 Pre/Pro
Main Amp
Rotel RMB-1066 6 chnl P-amp x 2
Additional Amp
Behringer DCX2496 x 2
Universal / Blu-ray / CD Player
OPPO BDP-103 Universal Player
Front Speakers
DIY SEAS H1456/H1212 Spkr x 5
Subwoofers
DIY JBL 2235H 15" SW x 2
Video Display Device
JVC DLA-X790R
Screen
Da-Lite Da-Snap 39105V - 92"
Wonderful speakers - the 3900's are ones that I would love to have.
Those are very capable down to a 40 Hz XO in a normal home environment. I will check out the timing based on the current data.
 

jtalden

Senior Member
Joined
May 22, 2017
Messages
427
Location
Arizona, USA
My AV System  
Preamp, Processor or Receiver
Marantz AV7705 Pre/Pro
Main Amp
Rotel RMB-1066 6 chnl P-amp x 2
Additional Amp
Behringer DCX2496 x 2
Universal / Blu-ray / CD Player
OPPO BDP-103 Universal Player
Front Speakers
DIY SEAS H1456/H1212 Spkr x 5
Subwoofers
DIY JBL 2235H 15" SW x 2
Video Display Device
JVC DLA-X790R
Screen
Da-Lite Da-Snap 39105V - 92"
The analysis found that the L and R mains are very smooth and flat when measured individually, but together (mono bass) there is a problem. There is a large SPL dip in the range from 65-105 Hz (see attached charts). This dip is caused by room effects that result in a large phase differential in this range. Panned L or R sounds will be fine, but mono bass notes in this important range will sound weak at the LP. There is an outside chance this is partially influenced by the Dirac EQ setup run, but probably not. you may want to consider moving FL/FR speaker positions and/or the LP position to see if different locations mitigate this issue. Room treatments may be effective if done well. An XO timing change at the 40 Hz XO will not help the current setup. The current timing is at the conventional initial target alignment. Typical timing adjustments were not helpful. A more favorable timing was found, but it was only with a large change in delay timing and the improvement was near the XO frequency. It did not significantly improve the problem frequencies.

If we want to use the the current speaker and LP locations then we could try to change the SW XO up to maybe 100 Hz. That has a good chance of providing some improvement.

31097


31098
 

lexicon

Member
Thread Starter
Joined
Nov 8, 2018
Messages
37
That's very interesting - thank you so much. As it happens I have been using a 100hz global crossover on the Arcam until the Storm arrived about ten days ago and I always found that that produced the best results in my room with that processor.

Alas I am unable to alter the speaker positions as they are aligned to the projection screen and one is in a corner. I will reset the crossover to 100hz and remeasure.

I appear to be one of the first people in the world (if not the first person) with the new Dirac Bass Management module and there are a number of people wanting to know if it fulfills it's claims. You run this after you set your curve and it calculates it's optimal crossovers. In my case these came out as follows:-

Mains 34hz (S3900s)
Centre 52Hz (Revel S16)
Surrounds 59Hz (Audiovector M1 Signature)
Heights 64hz (FH Revel S16 RH MK Sound ss150 tripoles)
Ceiling Atmos Mid Top 27hz!! (Monitor Audio)

Apart from the nonsensical proposed Xover for the in ceiling pair, your own anaysis would appear to indicate that these Xovers are unlikely to produce a good result in my room. If that's the case future users will need to be aware of that I think.

Fortunately, you can move the crossovers to your choice and recalculate the filters so I have tried this and saved the profile. I now have three profiles:-

1. 100hz crossovers no BM
2. Dirac BM calculated Xovers as above
3. Dirac BM reset to 100hx crossovers

I will attempt to load each one in turn and carry out the REW measurements from the same initial Dirac mic position and forward over the MDATs for each.

Interestingly Diirac has not altered the delays at all which would indicate that we are still going to have to revisit the delay question once the optimal crossover is found - as from what I understand from your analysis it seems that we need to determine the optimal crossover before we look again at whether the delays calculated by Dirac are correct/optimal themselves.

I have attached some screenshots that show what Dirac is doing.


Calculating.PNG


Calculating takes 5 mins or so

BM uncorrected.PNG


This is what dirac calculates crossovers at - see column on right. These show the uncorrected measurements

Main corrected.PNG


This shows the corrected curve after Dirac or at least purports to!

Centre corrected.PNG


Same for centre

Top corrected.PNG


And for heights with that 27hz choice of crossover

Main set at 100 Xover pre calc.PNG


This is what you see when you move the Xover up to 100hx - a new calculation is now needed

Main set at 100 Xover post calc.PNG


And now after that recalculation with crossover at 100hz - this is for mains as you can see on right

Storm BM applied delays.PNG


This shows delays have not changed from first Dirac measurement without any BM applied
 
Last edited:

jtalden

Senior Member
Joined
May 22, 2017
Messages
427
Location
Arizona, USA
My AV System  
Preamp, Processor or Receiver
Marantz AV7705 Pre/Pro
Main Amp
Rotel RMB-1066 6 chnl P-amp x 2
Additional Amp
Behringer DCX2496 x 2
Universal / Blu-ray / CD Player
OPPO BDP-103 Universal Player
Front Speakers
DIY SEAS H1456/H1212 Spkr x 5
Subwoofers
DIY JBL 2235H 15" SW x 2
Video Display Device
JVC DLA-X790R
Screen
Da-Lite Da-Snap 39105V - 92"
I will check the timing for the 100 Hz XO with BM.
The advantage to that option is that Dirac has effectively modified the 100Hz rolloff of both mains and SW to better follow a target LR-24 shape. Without this extra processing there is a significantly wider XO range. When using a 100 Hz the SW often can blead too much output into the upper bass where it may disrupt the smooth SPL response of the mains. This is not explained clearly so a hopefully the following charts will help.

31128


31129


31130


I will next check the timing results.
 

lexicon

Member
Thread Starter
Joined
Nov 8, 2018
Messages
37
I will check the timing for the 100 Hz XO with BM.
The advantage to that option is that Dirac has effectively modified the 100Hz rolloff of both mains and SW to better follow a target LR-24 shape. Without this extra processing there is a significantly wider XO range. When using a 100 Hz the SW often can blead too much output into the upper bass where it may disrupt the smooth SPL response of the mains. This is not explained clearly so a hopefully the following charts will help.

View attachment 31128

View attachment 31129

View attachment 31130

I will next check the timing results.
Thank you that’s very kind - it is very interesting to see what Dirac BM is doing and that it seems to be making a positive difference. I hope that using the higher Xover eliminates the mono bass issue?

The only other things I thought about that I could have tried for the mains at 40hz would be removing the bung from the port of the right speaker only or perhaps looking at inverting its phase before re-running Dirac? Or are both those ideas totally not worth entertaining?
 

jtalden

Senior Member
Joined
May 22, 2017
Messages
427
Location
Arizona, USA
My AV System  
Preamp, Processor or Receiver
Marantz AV7705 Pre/Pro
Main Amp
Rotel RMB-1066 6 chnl P-amp x 2
Additional Amp
Behringer DCX2496 x 2
Universal / Blu-ray / CD Player
OPPO BDP-103 Universal Player
Front Speakers
DIY SEAS H1456/H1212 Spkr x 5
Subwoofers
DIY JBL 2235H 15" SW x 2
Video Display Device
JVC DLA-X790R
Screen
Da-Lite Da-Snap 39105V - 92"
The only other things I thought about that I could have tried for the mains at 40hz would be removing the bung from the port of the right speaker only or perhaps looking at inverting its phase before re-running Dirac? Or are both those ideas totally not worth entertaining?
All the best advice is to let the SW handle the <80 Hz range for mono bass as that allows the bass SPL to be consistently smooth no matter the channel being played. For typical mains the SPL headroom is also greatly improved. The only downside for me is when the mains are designed to go low and it is then not being used. The mains could have been a lot less expensive if they are only designed for an 80 Hz XO. :(

I have been working on the timing. There is unusual timing problem between the FR and LF speakers. It most easily shows up in the measurement notes with the FL delay = -0.0089 ms and the FR delay = -5.0457 ms. A 5 ms difference makes no sense. The Lexicon chart in Post-12 shows more expected delay setting differences for a mic at the LP (2.88 and 2.74 ms). This also makes the accuracy SW timing suspect.

I am not sure why this 5 ms Impulse difference would occur. The first step is to take several measurements of the FL, FR and SW to confirm that the acoustic timing is working correctly. There should be no offset in the location of the impulses when viewed on the impulse overlay chart.

[I went ahead and found a favorable timing anyway based on the measurements, but there is no way to get us from the current timing to the new one when the the current timing doesn't make sense.]
 

lexicon

Member
Thread Starter
Joined
Nov 8, 2018
Messages
37
All the best advice is to let the SW handle the <80 Hz range for mono bass as that allows the bass SPL to be consistently smooth no matter the channel being played. For typical mains the SPL headroom is also greatly improved. The only downside for me is when the mains are designed to go low and it is then not being used. The mains could have been a lot less expensive if they are only designed for an 80 Hz XO. :(

I have been working on the timing. There is unusual timing problem between the FR and LF speakers. It most easily shows up in the measurement notes with the FL delay = -0.0089 ms and the FR delay = -5.0457 ms. A 5 ms difference makes no sense. The Lexicon chart in Post-12 shows more expected delay setting differences for a mic at the LP (2.88 and 2.74 ms). This also makes the accuracy SW timing suspect.

I am not sure why this 5 ms Impulse difference would occur. The first step is to take several measurements of the FL, FR and SW to confirm that the acoustic timing is working correctly. There should be no offset in the location of the impulses when viewed on the impulse overlay chart.

[I went ahead and found a favorable timing anyway based on the measurements, but there is no way to get us from the current timing to the new one when the the current timing doesn't make sense.]
That’s very strange. Using Dirac version 1 at 100hz I would need to add 10ms to every speaker and set the sub at about 2.8ms to get it to sound right. The mains ended up about 7.75ms behind the sub.

Listening to it now with only a 2.87 ms delay between sub and mains makes no sense to me when we know the sub already has a latency of 5-6ms. Anyway I will take some more measurements tomorrow to see if we can discover the cause of that 5ms difference between L&R.

Thanks again for all your help with this.

Jon
 

lexicon

Member
Thread Starter
Joined
Nov 8, 2018
Messages
37
Having examined the initial settings that existed on the processor before running Dirac further, I think I may know why that 5ms difference has arisen. I have a suspicion it’s the result of one of those lovely “undocumented features” of the processor :cool: . Before I share my theory I’ll effect the correction and remeasure.
 

lexicon

Member
Thread Starter
Joined
Nov 8, 2018
Messages
37
“All the best advice is to let the SW handle the <80 Hz range for mono bass as that allows the bass SPL to be consistently smooth no matter the channel being played. For typical mains the SPL headroom is also greatly improved. The only downside for me is when the mains are designed to go low and it is then not being used. The mains could have been a lot less expensive if they are only designed for an 80 Hz XO.“:(

The problem with that hypothesis as I see it is that you are relying on the sub (different make, construction, position and amplification) to provide the same ”quality” of bass as the stereo JBL mains. I can definitely hear the difference between the quality of sound produced from an SVS sub compared to a REL for example. Although the theory is that bass in not directional at those frequencies I’m not convinced one SVS sub located against my right wall can match the two expensively Class G amplified and biamped JBLs positioned at the front as regards lower mid bass quality. Seems a shame the JBLs will not produce good results with lower Xovers in my room but it is what it is I guess! It’s a living room so bass traps would not be an option.
 
Last edited:

lexicon

Member
Thread Starter
Joined
Nov 8, 2018
Messages
37
I have tried to reproduce the graph in your post 11 but cannot see how you arrived at that. What I was doing to look at combined mains was just clicking on the “average“ button which produces a nice even line! There is obviously more to it than that as your phase traces have (FDW) after them which (after hours of clicking tabs and buttons) seems to relate to the “frequency dependant window” in another set of “mind expanding” options reached from the IR tab at the top?

I can also see that there is a 14db variance between the left and right traces?

Without expecting you to teach me the entire REW “language” in a few minutes, would you be able to take me through your process steps so I can try to understand how that average line is arrived at and what must then be examined as regards phase angles etc. ?
 
Last edited:

jtalden

Senior Member
Joined
May 22, 2017
Messages
427
Location
Arizona, USA
My AV System  
Preamp, Processor or Receiver
Marantz AV7705 Pre/Pro
Main Amp
Rotel RMB-1066 6 chnl P-amp x 2
Additional Amp
Behringer DCX2496 x 2
Universal / Blu-ray / CD Player
OPPO BDP-103 Universal Player
Front Speakers
DIY SEAS H1456/H1212 Spkr x 5
Subwoofers
DIY JBL 2235H 15" SW x 2
Video Display Device
JVC DLA-X790R
Screen
Da-Lite Da-Snap 39105V - 92"
I used REW 'Trace arithmetic' which includes the impact of phase. The 'Average' button only considers the SPL. Had we measured left+right mains in that session we would have seen the the exact trace shown in the A,B average. The below screen capture recreates the process so you can see the REW controls used to create it.

The 14 dB difference in the legend is the SPL difference at the cursor position. The cursor is not shown in Post-11 so we do not know where it happened to be at the time the chart was saved. In the recreated chart below using the same FL, FR measurements the cursor is located at 27.13 Hz and thus this time the legend SPL is near 65 dB for both left and right.

31153


The overlay phase chart shown in Post-11 utilized a FDW of maybe 6 cycles. I don't remember the exact value used. It as done in order to clean up the traces a little. The same trend is easily see even without the FDW applied. It just has a few more wiggles due to inclusion of the later arriving sound.
 

lexicon

Member
Thread Starter
Joined
Nov 8, 2018
Messages
37
Wow thank you, that’s very clever stuff indeed. Is there a REW university anywhere that I can enrol at? :reading:
 

jtalden

Senior Member
Joined
May 22, 2017
Messages
427
Location
Arizona, USA
My AV System  
Preamp, Processor or Receiver
Marantz AV7705 Pre/Pro
Main Amp
Rotel RMB-1066 6 chnl P-amp x 2
Additional Amp
Behringer DCX2496 x 2
Universal / Blu-ray / CD Player
OPPO BDP-103 Universal Player
Front Speakers
DIY SEAS H1456/H1212 Spkr x 5
Subwoofers
DIY JBL 2235H 15" SW x 2
Video Display Device
JVC DLA-X790R
Screen
Da-Lite Da-Snap 39105V - 92"
I learned a lot from the REW help files. There is also supplement help for the beta versions. Those and possibly some other links can be found on the REW site.
 

lexicon

Member
Thread Starter
Joined
Nov 8, 2018
Messages
37
I learned a lot from the REW help files. There is also supplement help for the beta versions. Those and possibly some other links can be found on the REW site.
I'll keep reading!

Attached is the replacement MDAT with BM on 100Hz Xover + another with BM on at 80hz Xover lest you feel an inclination to compare that and let me know which you feel is best!

Please let me know if that spurious 5ms has gone.

Many thanks

Jon
 

Attachments

lexicon

Member
Thread Starter
Joined
Nov 8, 2018
Messages
37
I have just checked all the levels from my MLP using a Dolby Atmos test disc from Bluray. Alas the calculated levels are not good - similar to what used to be the case in V1.

I have had to raise the left surround by 6db to bring it up to the loudest speaker (Right Back Height).

The changes I have made to the front three are:-

Left Main +1.4db
Right Main +2.4db
Centre +2.4db

I am not sure whether you will wish to adjust for these when you look at the new profiles.This was from the 80hz Xover profile but I would expect the 100hz one to show similar results.

Jon
 
Top Bottom