Summary of Significant Accounting Policies (Narrative) (Details)	3 Months Ended		12 Months Ended
	Jul. 03, 2016 USD ($)	Apr. 03, 2016 USD ($)	Jan. 01, 2017 USD ($) shares	Jan. 03, 2016 USD ($)	Dec. 28, 2014 USD ($) shares	Dec. 29, 2013 USD ($)
Research and Development [Abstract]
Selling, general and administrative expenses include company-funded research and development			$ 167,700,000	$ 163,700,000	$ 166,900,000
Income Tax Disclosure [Abstract]
Number of years of cumulative operating income used to determine income tax valuation allowance			3 years
Accounts Receivable, Net [Abstract]
Reserve for doubtful accounts			$ 5,200,000	6,300,000
Expense of reserve for doubtful accounts			700,000	900,000	3,600,000
Cash and Cash Equivalents [Abstract]
Cash			98,600,000	85,100,000	141,400,000	$ 66,000,000
Cash equivalents held by foreign subsidiaries of Teledyne			95,200,000
Goodwill and Intangible Asset Impairment [Abstract]
Impairment of goodwill			0	0	0
Impairment of intangible assets			$ 1,000,000	500,000	700,000
Deferred Compensation Plan [Abstract]
Deferred compensation employee contribution vesting percentage			1
Deferred compensation liability			$ 47,400,000	43,900,000
Cash surrender value of life insurance			48,500,000	47,900,000
Accrual for Environmental Loss Contingencies Disclosure [Abstract]
Accrual for environmental loss contingencies			7,000,000	8,700,000
Supplemental Cash Flow Information [Abstract]
Cash payments for federal, foreign and state income taxes			24,600,000	86,500,000	72,700,000
Tax refunds received totaled			1,400,000	4,800,000	2,300,000
Cash payments for interest and credit facility fees totaled			23,600,000	24,200,000	17,600,000
Related Party Transactions [Abstract]
Related party transactions			0	$ 0	$ 0
New Accounting Pronouncements and Changes in Accounting Principles [Abstract]
Additional income tax benefits recognized as an increase to net income from adoption of accounting standard	$ 1,200,000	$ 600,000	$ 8,500,000
Percent of revenue - POC Method			30.50%	31.20%	28.70%
Shares excluded from computation of diluted earnings per share (in shares) | shares			0		0