Use of transformation coefficients

Affiliation
American Association of Variable Star Observers (AAVSO)
Fri, 04/01/2016 - 19:58

After imaging M67 I have determined the following transformation coefficients of my system:

filter band coefficients:

TB= 0.09162

TV=-0.0936

color index coefficients:

TBV=1.22732

I am using a 90 mm Apo refractor, V and B filter by Custom scintific made of colored dyed glass and the Atik 314 that mounts the Sony ICX 285 mono chip, that has little blue sensitivity as most consumer chips have.

I seem to recall a remark from Arne that states that filter band coefficients between 0.1 and -0.1 are great while color coefficients between 0.7-1.3 can be usable but with care (I maybe wrong with the statement of the actual range of the color coefficient however).

Now, as most of my observing program actually covers red stars such as Miras and SR stars I wonder if I can use those transformation with no additional thought or if I need to exercise some care in the transformation. If the latter applies I need some help in understanding what procedure should be applied. I could see from the AAVSO survey that TBV = 1.22 is in line with many observers.

Thank you for your help

 

Gianluca 

 

Affiliation
American Association of Variable Star Observers (AAVSO)
Coefficient Range

Hi Gianluca:

It is nice to obtain color coefficients that range from 0.9 - 1.1 BUT YES, some observers have reported systems with larger coeffs such as you found for your system. It would be nice if all observers who have generated transform coeffs would take the survey and report their coeffs and system characteristics BUT I guess it would take a request/order from Stella or Arne!  frown

So, IMHO there is no reason not to use the ones you generated. It would be good to test them by taking some images, changing some comps (with high color) to targets (VPhot), measuring their transformed magnitudes using your values and see how they agree with the reported standard magnitudes. This is the type of CARE that everyone should take along with always looking at the data!  wink

Ken 

Affiliation
American Association of Variable Star Observers (AAVSO)
Checking transformation coefficients

Hi Ken,

I have checked some of my images with VPHOT to see how my transformed magnitudes match the known magnitudes of several comparison stars in the fields. The result is encouraging as for most stars the differences lie between the uncertainty listed in the photometry tables. So far I have measured comp stars with color index B-V up to around 1.5.

Gianluca 

Affiliation
American Association of Variable Star Observers (AAVSO)
Transform vs Non-transform

Hi Gianluca:

Good, although you did use the qualifier "most"! How do the transformed and untransformed magnitudes compare to the known standard magnitude? This gives you an idea how significant transformation is or is not. IF the comp and target had the same color, the difference should be negligible.

Ken

Affiliation
American Association of Variable Star Observers (AAVSO)
Transform vs. Non-transform

Hi Ken,

I have continued measuring various stars in the fields and I think I have now got a good number of measuring of both transformed and non transformed stars. Actually the transformed magnitudes appear much closer to the standard values listed in the photometry tables and, aside from a couple of stars, all transformed results appear to be within the uncertainty range listed in the tables. The two stars that are off are actually so by about 0.02 mag above uncertainty and they are still off when magnitudes are untransformed. I think I can conclude that applying transformation coefficients delivers better accuracy at least with my system.

Gianluca

Affiliation
American Association of Variable Star Observers (AAVSO)
Confirmation

Gianluca:

I'm glad that you have convinced/proven to yourself (and others) that your transformation coeffs give more accurate magnitudes. I'm sure Arne is smiling too!

Ain't science grand (at least most of the time)!  laugh

Ken

Affiliation
American Association of Variable Star Observers (AAVSO)
Transforming standard star observations

Note that TransformApplier has a feature that helps you build confidence in your transform coefficients. If you check the box "Test TC" on the Application Tab  TA will will move your check star into the target location of your observation record and then transform using the comp star. You can then examine the Report Tab to see how well your observation data and transformation were able to match the reference data for the check star. The rational here is that if you can't measure a known star well, then your measurements of variable stars are suspect.

George

Affiliation
American Association of Variable Star Observers (AAVSO)
Transformation coefficients

Thank you for the hint George. Just a quick question. Can I use an ensemble with the "Test TC" application or shall I use just one comp star? I generally use ensemble photometry with VPHOT.

Gianluca

Affiliation
American Association of Variable Star Observers (AAVSO)
Transforming standard star observations

To:  George,

Just as a "realty check" for the transform coefficients I produced from TG on M67 data I took,  I did as you indicated in TA's "Test TC." 

My average (of 15) transformed magnitude differences for B, V, & I were 0.73%, -0.27%, and -0.14% for the TU Lyn field star 000-BBL-384. These have published BVI mags 11.608, 10.349, & 8.961 vs my (average of 15) transformed BVIs of 11.689, 10.321 & 8.949 respectively. 

I have to point-out that the filters I used for B & V are not standard filters, but Astrodon Blue and Green filters; the I is an old Schueler glass Ic photometric filter (showing the least amount of %error).  I have these in my 2nd SBIG camera (ST-8XE).  My ST-10XME camera has the Astrodon photometric filters, but I was using that camera for spectroscopy.  I'll test those Astrodon photometrics as well and see if the differences are smaller.

James 

Affiliation
American Association of Variable Star Observers (AAVSO)
BGI Transform Difference

Hi James:

You noticed that the transformed magnitudes agree more poorly for the Blue (0.08 mag) and Green (0.03) filters compared to the cousins I filter (0.01). I would have hoped/expected that the difference from standard magnitudes was closer to +-0.01 mags for all the filters after transformation. So either the coeffs are  a bit suspect or the target's energy distribution due to emission or absorption lines causes some issues. How far off are the untransformed magnitudes with an ensemble? Comments?

Ken

Affiliation
American Association of Variable Star Observers (AAVSO)
BIG Transform Difference

To Ken,

Thanks for the look!  This TU LYN is probably a poor field for me to test ensemble mags.  Since my C-11/ST-8XE system doesn't have an off - axis guider, I was forced to guide "thru the filters" and had the target and only two comp stars in the fov.  I'll try on a different more generous target (5 or more comps in fov) and also run the TA option again to get an average transformed magnitude on a comp.  I'll post my Trans Coefficients after I get back from work.

James

Affiliation
American Association of Variable Star Observers (AAVSO)
Transform Coeffiecients

Here are the transform coeffieicents for my C-11/ST-8xe CCD with a F6.3 reducer & Astrodon RGB and Schueler Ic filter and my CDK17/ST10xme CCD & Schueler Rc, Astrodon VBI (from 4x60sec1x1 bin shots on M67 thru filters using Vphot & TG):

 

 

 

C-11/ST-8xe(Astrodon RGB & Schueler Ic)    CDK17/ST10xme(Schueler Rc, Astrodon VBI)   

     

Tbv:     1.554 +/- 0.017                                 1.384 +/- 0.023

Tb_bv: 0.348 +/- 0.015                                 0.368 +/- 0.027

Tv_bv:-0.009 +/- 0.011                                  0.091 +/- 0.048

Tvr:     0.982 +/- 0.026                                  1.246 +/- 0.030

Tv_vr: -0.020 +/- 0.024                                 0.191 +/- 0.106

Tr_vr: -0.002 +/- 0.027                                 -0.006 +/- 0.093

Tri:      1.016 +/- 0.040                                  1.095 +/- 0.068

Tr_ri:   0.001 +/- 0.034                                  0.006 +/- 0.115

Ti_ri:  -0.014 +/- 0.042                                 -0.081 +/- 0.070

Tvi:     0.992 +/- 0.020                                  1.163 +/- 0.034

Tv_vi: -0.011 +/- 0.013                                  0.107 +/- 0.059

Ti_vi:  -0.003 +/- 0.019                                 -0.033 +/- 0.031

Tr_vi: -0.000 +/- 0.015                                  -0.001 +/- 0.052

Except for the Tbv these transform coeffecients are equal to smaller than the transform coeffecients from my CDK17 system using the ST-10xme CCD and Astrodon "photometric" BVI filters!  The night (15Feb16) I shot with the CDK17 might have had worse seeing and the 17" apeture is more suseptible to this.

James

Affiliation
American Association of Variable Star Observers (AAVSO)
Transformation coefficients

Hi James,

although I am not as expert as others, both Tbv and Tb_bv look pretty large to me. It would be interesting to see results by others with similar setup.

Cheers

Gianluca

Affiliation
American Association of Variable Star Observers (AAVSO)
Transformation coefficients

To:  Gianluca,

RE:"....both Tbv and Tb_bv look pretty large to me."

Yes, even Dr. Arne mentioned that a year or two ago.  I believe those transforms are correct based on my observation of spectra I've taken with the ST-10xme CCD sensor.  H-y and shorter wavelength Balmer lines are very dim in my images showing my sensor is not very sensitive to the deep blue.   Here is a sample spectra (spectrally calibrated/instrument response un-corrected) taken with my ST-10xme attached to an L-200 spectroscope on my CDK17 reflector: http://www.astroimage.info/files/a%20Can%28micro1400%29spectra17Apr16.jpg

Although the line-spectra "looks good" looking at it 2-d .FITS image at top shows tremendous light loss when you go leftwards past the H-y line (about 434nm).  Maybe my ST-10xme is really and ST-10xe!  Coincidently, the ST-8xe shows similar (little worse) blue response in the transforms coefficients.

James

p.s. The "bifurcation" in the 2d spectra image is from the acromatic covergence lens in the spectra scope.  The CDK17 (when use for photometry) is fully corrected across a 50mm image plane.

Affiliation
American Association of Variable Star Observers (AAVSO)
Ken's transform survey

Ken,

Could you please post the link(s) to your transform survey both for submitting transforms and for viewing the database.

Phil

Affiliation
American Association of Variable Star Observers (AAVSO)
Transformation coefficients

Hi Ken,

good advice. I will be doing it shortly and I will report the results.

Gianluca

Affiliation
American Association of Variable Star Observers (AAVSO)
Transformation Coefficients

Here is my set-up:

Telescope:    Meade 0.4m SCT-ACF w/Optec .7x FRFF
CCD:         QSI516
Filters:    AstroDon BVRI

M67 images (4xB, 4xV, 4xR, 4xI) were acquired under very good transparency and seeing conditions, at airmass ~1.2, binned 2x2 and fully calibrated.

I just started to use Gord Myers' TG program. Very nice indeed. I can't recommend enough to use VPhot to generate the reports for TG; very fast and efficient. I am brand new to transformations, and these are my first time results (copied from TG-generated ini file):

Tbv= 1.134
Tb_bv= 0.135
Tv_bv= 0.012
Tvr= 1.019
Tv_vr= 0.022
Tr_vr= 0.015
Tri= 1.123
Tr_ri= 0.036
Ti_ri= -0.082
Tvi= 1.058
Tv_vi= 0.014
Ti_vi= -0.036
Tr_vi= 0.011
[Error]
Tbv= 0.019
Tb_bv= 0.020
Tv_bv= 0.009
Tvr= 0.019
Tv_vr= 0.019
Tr_vr= 0.024
Tri= 0.034
Tr_ri= 0.028
Ti_ri= 0.023
Tvi= 0.012
Tv_vi= 0.010
Ti_vi= 0.011
Tr_vi= 0.013
[R Squared Values]
Tbv= 0.981
Tb_bv= 0.375
Tv_bv= 0.014
Tvr= 0.961
Tv_vr= 0.011
Tr_vr= 0.003
Tri= 0.903
Tr_ri= 0.011
Ti_ri= 0.095
Tvi= 0.985
Tv_vi= 0.015
Ti_vi= 0.086
Tr_vi= 0.005

Affiliation
American Association of Variable Star Observers (AAVSO)
Hi all

Hi all

New to transforms here as well.

Rig is 8" Meade SCT with ST8XME Bessel BVI

NGC7790 and M67 are solved and calibrated with MaxIm

VPHOT average-stacks 5 to 9 images depending on how many get weeded out.

Stacked images get the VPHOT treatment where I delete 1/2 to 2/3 with low S/N. I also delete the ones with stars in the outer ring that is supposed to be sky. No comps or checks or variables are selected (That was a hard thing for me to realize).

The B, V, and I VPHOT files are imported into TG5. I examine each line for outlyers and delete points to sort of minimize the 2-sigma while retaining a meaningful slope by eye. Then 3 M67's and 3 NGC7790's transforms were averaged. Some were taken in dark skies, some in moonlit skies (there seems to be a small difference but I have not studied it yet). 

Result

Tbv      1.260         err=0.116          r^2= 0.96

Tb_bv  0.141        err=0.048          r^2= 0.65

Tv_bv -0.049         err=0.045          r^2= 0.55

Tvi       0.963         err=0.120          r^2= 0.93

Tv_vi  -0.050         err=0.049          r^2= 0.57

Ti_vi   -0.019         err=0.0.065       r^2= 0.07

Could experts here comment on whether these look reasonable? Have not yet loaded TA or done the match to a known AUID or comp.

Ray

 

Affiliation
American Association of Variable Star Observers (AAVSO)
Coeffs Reasonable

Ray:

Based on what I have seen from others, your coeffs look "reasonable".  :-)

A little note about procedure might make things easier:

1. Although I am a believer in selecting std field comps that show little impact by companion stars in the apertures, removing 1/2 to 2/3 of the standard comps is probably unnecessary (or worse). I have generally given up such a preliminary effort. That is, just keep ALL the standard field comps and let TG show which are outliers at the SNR you choose (e.g. default = 20 (SNR)). It is so easy to visually delete those comps that are outside the 2 SD lines. This allows you to keep those that are statistically acceptable and especially keep comps at the color extremes. This really helps since it is the comps that are at the ends of the slope lines that help define the slope best! Note also that VPhot mathematically removes the impact of extraneous stars in the sky aperture.

2. The main caution is not to remove too many comps that exist outside the revised 2 SD. As you remove comps from the original population, the SD is recalculated and represents the error limits for the new population. At some point this does not represent the original population and becomes inappropriate. I do remove the remaining "obvious" comps that are clearly outside the revised 2 SD lines BUT I am very cautious about this. I usually keep about 70+ comps? Consider imaging longer if most of the comps are too faint.

3. I usually do not generate average coeffs from both M67 and NGC7790 together. I generate an average for each cluster and compare how they have changed if at all. They are of course about 6 months apart in time and your system may have changed a little?.

4. My color coeffs (~1) usually give r^2 values a bit closer to 0.99 than you got. The r^2 for the filter coeffs (~0, horizontal line) should mathematically be 0.00 not 0.99 so don't obsess about what you got. As soon as the slope moves away from 0 (even by a small amount), the r^2 is dramatically changed from 0 and tries to report the correlation assuming that the line has a tight (or not tight) non-zero slope.

5. The whole process is a bit more art than I think it should be but I do see little (within error) change over the year with my system.

6. As Phil (spp) asked I'll try to post the transform survey links again AND make it a sticky post this time.  I guess over the years we might get a reasonable number of participants?

Ken

 

 

 

Affiliation
American Association of Variable Star Observers (AAVSO)
Thanks Ken

Thanks Ken

1. I was aware that TG could set a S/N limit, so , will run them all again with all standard stars and a lower limit on S/N. I forgot that VPHOT had an algorythm to avoid stars in the sky rings.

2. I was left with 10 to 20 comps. Average stacking doesn't gain me much. PEC is not working here yet, so I am limited to about 40 second exposures.

3. NGC7790 and M67 coeficients are consistantly different. Should that tell me that there are limits to the accuracy of standards accross the sky?

4. I once understood the meaning, significance and application of color vs filter coefficients, but I don't know a handy reference to quickly refresh my understanding. I should be familiar enough with the arithmatic to cough up the answers at any geiven moment, but I'm lazy and just want to crank out transformed data (given a little due care for process quality).

5. Yup, it is artfull.

6. I would like to see that survey and participate in it.

Ray

 

Affiliation
American Association of Variable Star Observers (AAVSO)
After comparing methods:

After comparing methods:

I get similar values and errors when picking good stars in VPHOT or using all of them, then filtering out S/N < 20 or 30 or 40 (depending on the exposure and number of stars available). Filtering works on both ends.

I get most consistant results if I minimize the error when weeding outlyers in TG 5.10.  It helps to blow up the little fit plots to full page so that no outlyers are hidden in the plot's text and so that points are more seperated on the screen. I can't tell which stars that I am deleting in TG5, but I can see where they are in color. I can tell which stars that get deleted in VPHOT, but I need the photometry to discern colors.

To high a SN threshold leaves to few stars for an accurate slope. ie, the slope can change suddenly when only looking at a few stars. Looks like loss of color distribution.

M67 yields slighlty different results than NGC7790 under several circumstances. Need to get a feel for how that changes transformed magnitudes. . . 

I trust M67 results more because there are more stars above SN thresholds and maybe the color distribution is better.

Affiliation
American Association of Variable Star Observers (AAVSO)
Are your transform coefficients good?

It's really hard to tell just by looking at the coefficients if they are good. Nominally the color coefficients (Txy) should be 1.0 and the magnitude coefficients (Tx_yz) would be 0 for a "standard" system. Understanding your camera's sensor might help explain coefficients that seem high or low.

The real test is if it improves your measurements. Does your measurement of a magnitude match a reference value within the error bars? TA ( https://www.aavso.org/transform-applier ) has a feature where it helps you do this: If you check the "TestTC" the program will apply your transforms to the check star instead of the target star. The report tab will compare your measurement, and transformed measurement, to the reference value. That is the test: if you can't duplicate a magnitude of a known constant star, you really need to question if you have an accurate measurement of a variable star.

This report in TA is still pretty primitive. I would be delighted if some statistics savvy astronomer could help me design a "goodness" test for this measurement. Does the transform move the the result toward the reference value? Does the transformed result accurately match the reference within the error bars? What should you do if there is a bad match? This would improve our ability to judge our transform coefficients.

George

Affiliation
American Association of Variable Star Observers (AAVSO)
Yup, I need to learn the TA

Yup, I need to learn the TA next, and I am sure to try the TestTC feature. Got it all loaded and ready to run.

I am thinking that it will give good feedback as to whether my transforms are OK.

I am learning many things. Like making and saving calibration files in MaxIm so that I use the most pertinent flats, exposure of flats vs. ADU counts and the effects application of various ADU counts, etc. I used to do calibration in AIP4WIN, but forgot how after 6 years of inactivity. It has taken a year to get the mount, telescope, focuser, camera, filters, computers, software, observatory up and running again. MaxIm makes me nervous becaise it's mechanisms are not readily transparent. I take some solace from rumors that AAVSO helped check their code. Also, once due care is taken with calibration files, the calibrated images "look" calibrated under some scrutiny. 

As to your last paragraph, all the easy stuff has been done in physics and astronomy.  The hard stuff remains. So every astronomer that I know, knows statistics like the back of their hands. Goodness and Bayesian probabilities are just a necessary process to validate results for datasets.  For the average Joe user like me, an easy to use trouble-shooting guide would be a usefull answer to your question: "What should you do if there is a bad match?" That would improve our ability to judge our transform coefficients."

Thanks again George, I'll get TA cooking when I can get to it. The telescope can sure crank out a lot of stars and BVI's. Got a TON of observations to transform, but still not enough time to get to it. Perhaps I can eventually send results for your survey that might be useful to those learning like I am now.

Ray

Affiliation
American Association of Variable Star Observers (AAVSO)
TG5.10 star deletion message

When you delete a star in TG5.10, there is a message at the bottom of the screen identifying which star was deleted.  The attached screen capture shows the message highlighted in a red box.

Gordon

Affiliation
American Association of Variable Star Observers (AAVSO)
Thanks Gordon

Thanks Gordon

I failed to notice it. One thing is obvious when comparing your Tb_bv plots to mine is that you get more stars  with greater b-v range.  Do you have Bigger optics? The accompanying figures were done with >6 images stacked, all standards included, and S/N > 20.  8" SCT having a "solved" focal length of 1405 mm. I often get both NGC7789 and NGC7790. Your vertical scale is much tighter than mine. Your S/N must be generally better. Bigger optics? 

I wonder if I switched back to the Megrez 80mm whether the cluster images would be big enough to pick apart, so as to get any accuracy of transforms. I suppose it could be done with long enough exposures and a perfect mount.  I think my images so far may be good enough to do/learn the exercise. I'll fire up TA today.

Affiliation
American Association of Variable Star Observers (AAVSO)
Number of reference stars

I cheated on you - the plot I showed was from the M11 standards field which has more comps than M67.  Also, I have a17 inch scope.  Attached is my Tbv plot using M67 - I get over 150 stars

Affiliation
American Association of Variable Star Observers (AAVSO)
17 inch gets lots of stars.

17 inch gets lots of stars.

I did a 1st TA today, finally getting some data out and, i think, a happy Test TC. However, email to  Geroge shows no B data transformed. Though it might be order of input BVI files, but no fix there. More struggling to be done.

Ray

Affiliation
American Association of Variable Star Observers (AAVSO)
Problems with grouping in TA

Ray,

When transforming your obs the rule is that you are supposed to explicitly group your observations with the GROUP field. If you want to trust the software to do it for you need to have all the obs use the same value in the GROUP field (eg "na"). In that case the software make its best effort to group the data into sets.

In your situation the B data was group "na" but the V and I was in group "4". So, they were kept separate: The VI transformed together and the B was left by itself, un transformed.

George

 

Affiliation
American Association of Variable Star Observers (AAVSO)
New transformation coefficients

After getting a new filter set (BVI from Custom Scientific) and a new CCD I have imged M67 to determine the new transformation coefficients. I have used 49 stars with VPHOT and got the following coefficients (same sequence of stars for all three filters):

 

Filter band coefficients:

 

Tb (B-V) = 0.2397

Tv (B-V) = -0.0841

Ti (V-I) = -0.0201

Tv (V-I) = -0.0903

 

color coefficients:

 

Tbv = 1.4789

Tvi = - 0.9343

 

As you can see the Tb and Tbv coefficients are large while the Ti and Tvi look pretty small to me. The scope  I am using is a 90 mm Apo refractor (doublet with FPL53 glass) and the CCD is the Atik 383 (kaf 8300 sensor). The CCD has little sensitivity to blue so a bigger coefficient may be expected here.

 

After upgrading the new coefficient in VPHOT I have done some photometry. To see how well the transformed magnitudes macth with the standard system (from the AAVSO sequences) I have measured a couple of stars in the field of variable star U Persei whose color index (B-V) is around 0.6-0.7.The results seem pretty good to me.

 

Instead I am puzzled about the magnitudes I am getting for red stars (most of the variables I am following are red), particularly as I am getting very different results in V by using B-V vs. V-I transformation. Here is an example:

 

S PERSEI (ensemble photometry of 5 stars with VPHOT):

B = 13.287 (err.0.040)
V = 10.487 (err. 0.055)  (B-V transformation)
V = 10.345 (err. 0.051) (V-I transformation)

I = 6.006 (err. 0.076)

 

Untrasformed magnitudes of S PER with same sequence of stars (VPHOT):

 

B = 12.736 (err 0.049)    very different from the transformed magnitude

V = 10.680 (err. 0.049)  very different from the transformed magnitude

I = 6.079 (err. 0.075)  pretty small difference

I have chosen a mag.10 star as check star (AUID 000-BBD-742) and here is what I am getting:

standard mag by AAVSO sequence B=10.349 (err.0.072) V = 10.015 (err 0.051)  I = 9.570 (err. 0.090)

measured magnitude by using the sequence of stars (VPHOT): B = 10.425  V = 10.020 (B-V) 10.024 (V-I)  I = 9.521

non transformed measured magnitude with same sequence of stars (VPHOT): B = 10.448 (err. 0.044) V = 10.012 (err 0.049) I = 9.518 (err 0.078).

About this check star I can see that both the transformed and non trasformed magnitudes differ in B by about 0.1 mag from the standard mag listed in the AAVSO sequence (that has an uncertainty of 0.072 mag however). And I can also see that there is a big difference in the V magnitude of S PER (0.142 mag) depending on which transformation is used (B-V or V-I). The same thing appears with other red stars. The V-I transformation delivers brighter mag in V compared to the B-V transformation. Of course I understand that there is a problem somewhere as it is strange to get 2 different results in V and I don't know which of the 2 mag in V is more realistic.

Thank you for your help

 

Gianluca

 

 

 

 

 

 

Affiliation
American Association of Variable Star Observers (AAVSO)
S Per

Hi Gianluca,

Unfortunately, S Per is a bad choice for this experiment!  If you look at the sources for the photometry, B comes from Tycho2 (normally ok), but V comes from TASS (sometimes ok).  Then (B-V) is formed by using these two dissimilar catalogs.  If you just use Tycho2 for the B and V values, appropriately transformed, you get for your check star 000-BBD-742:

B=10.357   V=10.000

with errors around 0.03mag (probably a little underestimated, at this faintness).  The V-band result matches pretty well between TASS and Tycho2, and your transformed result also matches, using either (B-V) or (V-Ic) for the transform color.  Good!  TASS and Tycho2 don't always agree.

Your transformed B value doesn't agree perfectly; it is 0.07mag fainter than the catalog value, but it lies formally within 1 or 2 sigma of the catalog value, which is also ok.  So your check star results are actually pretty good.

Where you see the biggest difference is on S Per itself.  Unfortunately, this is to be expected, and is why red stars are so difficult.  Note that the (B-V) value for S Per is around 2.8 or so, which is outside of the range that you used for your transformation coefficient determination in M67.  (V-Ic) is worse, being around 4.6.  Often transformations get non-linear when you go far outside your transformation region, and this is especially true for filters that don't closely match the standard, such as your B filter.  For normal stars, (V-Ic) ~ 1.1*(B-V), and you can see that this relationship doesn't hold.  This is because S Per is an M supergiant, with lots of structure in its spectrum, especially near minimum light.  Most of the structure is in the red part of the spectrum.  That makes it difficult to transform using (V-Ic).  Yet, because of its faintness at B, many observers can't use (B-V).  So you will most likely see two light curves from CCD observers, offset from one another depending on which filters they used to transform their data.  I don't know a good solution to this.  My recommendation is to include a note on the observation indicating what color index you used for your transformation.  Another possibility is to average the results from the two techniques.

Bottom line:  I'm glad to see you transforming your data!  For normal stars, the technique will improve your results.  For stars that lie outside of your transformation region, you may see differences between methods.

Arne