The Part 121 regulation that governs low visibility takeoffs are specified in 14 CFR 121.651. It references company OpSpecs and 91.175 and Part 97:
"Standard" takeoff minimums are specified in 14 CFR 91.175 and would be the highest of:
OpSpec C056 is issued to all 121 carriers, and basically just spells out the "standard" takeoff minimums that I listed above, and specifies that RVR must be used if it is available on the runway.
OpSpec C078 is normally issued and allows taking off with lower than standard visibility as long as the airport doesn't already have published higher than standard takeoff minimums. This is a fairly involved OpSpec with several optional paragraphs, and operators may be approved for takeoff operations down to and including 300 RVR. For those not familiar with the term, RVR (Runway Visual Range) is the distance that a pilot can see down the runway, measured by automatic equipment, and is measured in feet in the US.
§121.651 Takeoff and landing weather minimums: IFR: All certificate
holders.
(a) Notwithstanding any clearance from ATC, no pilot may begin a
takeoff in an airplane under IFR when the weather conditions reported
by the U.S. National Weather Service, a source approved by that
Service, or a source approved by the Administrator, are less than
those specified in—
(1) The certificate holder's operations specifications; or
(2) Parts 91 and 97 of this chapter, if the certificate holder's
operations specifications do not specify takeoff minimums for the
airport.
§91.175 Takeoff and landing under IFR.
...
(f) Civil airport takeoff minimums. This paragraph applies to persons
operating an aircraft under part 121, 125, 129, or 135 of this
chapter.
(1) Unless otherwise authorized by the FAA, no pilot may takeoff from
a civil airport under IFR unless the weather conditions at time of
takeoff are at or above the weather minimums for IFR takeoff
prescribed for that airport under part 97 of this chapter.
(2) If takeoff weather minimums are not prescribed under part 97 of
this chapter for a particular airport, the following weather minimums
apply to takeoffs under IFR:
(i) For aircraft, other than helicopters, having two engines or less—1
statute mile visibility.
(ii) For aircraft having more than two engines—1⁄2 statute mile
visibility.
(iii) For helicopters—1⁄2 statute mile visibility.
C056, IFR Takeoff Minimums, Part 121 Airplane Operations - All
Airports.
a. Standard takeoff minimums are defined as 1 statute mile visibility
or RVR 5000 for airplanes having 2 engines or less and ½ statute mile
visibility or RVR 2400 for airplanes having more than 2 engines.
b. RVR reports, when available for a particular runway, shall be used
for all takeoff operations on that runway. All takeoff operations,
based on RVR, must use RVR reports from the locations along the runway
specified in this paragraph.
c. When a takeoff minimum is not published, the certificate holder may
use the applicable standard takeoff minimum and any lower than
standard takeoff minimums authorized by these operations
specifications. When standard takeoff minimums or greater are used,
the Touchdown Zone RVR report, if available, is controlling.
d. When a published takeoff minimum is greater than the applicable
standard takeoff minimum and an alternate procedure (such as a minimum
climb gradient compatible with aircraft capabilities) is not
prescribed, the certificate holder shall not use a takeoff minimum
lower than the published minimum. The Touchdown Zone RVR report, if
available, is controlling.
C078, IFR Lower Than Standard Takeoff Minimums, 14 CFR Part 121 Airplane Operations - All Airports.
Standard takeoff minimums are authorized in operations specification
paragraph C056. The certificate holder is authorized to use lower than
standard takeoff minimums in accordance with the limitations and
provisions of this operations specification as follows.
a. Runway visual range (RVR) reports, when available for a particular
runway, shall be used for all takeoff operations on that runway. All
takeoff operations, based on RVR, must use RVR reports from the
locations along the runway specified in this paragraph.
b. When takeoff minimums are equal to or less than the applicable
standard takeoff minimum, the certificate holder is authorized to use
the lower than standard takeoff minimums described below:
(1) Visibility or runway visual value (RVV) ¼ statute mile or
touchdown zone RVR 1600, provided at least one of the following visual
aids is available. The touchdown zone RVR report, if available, is
controlling. The mid RVR report may be substituted for the touchdown
zone RVR report if the touchdown zone RVR report is not available.
(a) Operative high intensity runway lights (HIRL).
(b) Operative runway centerline lights (CL).
(c) Serviceable runway centerline marking (RCLM).
(d) In circumstances when none of the above visual aids are available,
visibility or RVV ¼ statute mile may still be used, provided other
runway markings or runway lighting provide pilots with adequate visual
reference to continuously identify the takeoff surface and maintain
directional control throughout the takeoff run.
[NOTE: If an operator is not authorized RVR 1000 the POI will not
select RVR 1000 in the OPSS. If the OPSS is not available the POI
should delete subparagraph b(2), b(3), & b(4) from the word
boilerplate.]
(2) Touchdown zone RVR 1000 (beginning of takeoff run) and rollout RVR
1000, provided all of the following visual aids and RVR equipment are
available.
(a) Operative runway centerline lights (CL).
(b) Two operative RVR reporting systems serving the runway to be used,
both of which are required and controlling. A mid-RVR report may be
substituted for either a touchdown zone RVR report if a touchdown zone
report is not available or a rollout RVR report if a rollout RVR
report is not available.
[NOTE: If an operator is not authorized RVR 500 the POI will not
select RVR 500 in the OPSS. If the OPSS is not available the POI
should delete subparagraph b(3), & b(4) from the word boilerplate.]
(3) Touchdown zone RVR 500 (beginning of takeoff run), mid RVR 500,
and rollout RVR 500, provided all of the following visual aids and RVR
equipment are available.
(a) Operative runway centerline lights (CL).
(b) Runway centerline markings (RCLM).
(c) Operative touchdown zone and rollout RVR reporting systems serving
the runway to be used, both of which are controlling, or three RVR
reporting systems serving the runway to be used, all of which are
controlling. However, if one of the three RVR reporting systems has
failed, a takeoff is authorized, provided the remaining two RVR values
are at or above the appropriate takeoff minimum as listed in this
subparagraph.
(4) At foreign airports which have runway lighting systems equivalent
to U.S. standards, takeoff is authorized with a reported touchdown
zone RVR of 150 meters, mid RVR of 150 meters, and rollout RVR of 150
meters. At those airports where it has been determined that the runway
lighting system is not equivalent to U.S. standards, the minimums in
subparagraphs a(1) or (2), as appropriate, apply.
c. Takeoff Guidance System, If Applicable. If the certificate holder
is authorized to use takeoff minimums based upon the use of takeoff
guidance systems, the minimums will be specified for the aircraft
listed in the Table 1 below. The certificate holder shall conduct no
other takeoffs using these takeoff minimums. If subparagraph c is not
authorized, N/A will be annotated in each of the columns in the table.
(1) Special provisions and limitations.
(a) Operative high intensity runway lights (HIRL).
(b) Operative runway centerline lights (CL).
(c) Serviceable runway centerline markings (RCLM).
(d) Front course guidance from the localizer must be available and
used (if applicable to guidance systems used).
(e) The reported crosswind component shall not exceed 10 knots.
(f) Operative touchdown zone, and rollout RVR reporting systems
serving the runway to be used, both of which are controlling, or three
RVR reporting systems serving the runway to be used, all of which are
controlling. However, if one of the three RVR reporting systems has
failed, a takeoff is authorized, provided the remaining two RVR values
are at or above the appropriate takeoff minimum as listed in this
subparagraph.
(g) The pilot-in-command and the second-in-command have completed the
certificate holders approved training program for these operations.
(h) All operations using these minimums shall be conducted to runways
which provide direct access to taxi routings which are equipped with
operative taxiway centerline lighting which meets U.S. or ICAO
criteria for CAT III operations; or other taxiway guidance systems
approved for these operations.
(2) The certificate holder is authorized to use the following takeoff
minimums for the airplanes listed below.
Table 1 (N/A = Not Authorized) Airplane M/M/S Lowest Authorized RVR
Required Takeoff Guidance System
[NOTE: If an operator is not authorized pilot assessment the POI will
not select this statement in the OPSS. If the OPSS is not available
the POI should delete subparagraph d in its entirety from the word
boilerplate.]
d. Pilot Assessment of RVR for Takeoff (if applicable). In
circumstances when the touchdown zone RVR reporting system has failed,
is inaccurate, or is not available, the certificate holder is
authorized to substitute pilot assessment of equivalent RVR for any
touchdown zone RVR report required by this operations specification
paragraph provided that:
(1) The pilot has completed the FAA-approved training program for
visibility assessment in lieu of RVR, and
(2) Runway markings or runway lighting is available to provide
adequate visual reference for the assessment.
